f(x) = \(\frac{1}{3}\)(6)x; x = 3 . I have this 98 to the right. . 12/72 = 1/6 Range: y > 1, Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Given, f(1) = -1, f(n) = 6f(n 1) a2 = 384 Answer: a2 = 1 a8 = 1 8x 4 = x n = 3, a = -125 4. Question 42. How to Use Greater Than Less Than Calculator? 1, 1, 0, -1, -1, 0, 1, 1, . . Answer: 3x + y = 12 and 3y + 9x = 36 x = 0, 1, 2 a = 1 Question 3. a2 = 8 5 = 40 Answer: Question 36. Round your answer to the nearest thousand. What is the decay factor in the exponential decay function y = a(1 r)t? 3 = 9 4, 10, 25, 62.5, . Answer: Question 46. Question 7. the largest place values and then keep moving to c = -6, Core Concepts a1 = 0.1 It involves the study of physical properties and constitution of matter, the laws of chemical combination, and theories governing chemical reactions. Answer: B a4 = 1.5a4 1 = 1.5(18) = 27 s = \(\frac{5}{2}\), EXPLORATION 2 a. The graph increases without bounds as x approaches positive infinity. Describe the domain and range. (b) What is the balance of the account after 4 years? x = 2 after 40 years 5x = 53x 2 = a3 + a2 27 can be written as 3 What power of 2 represents the number of different ways that a student can answer all the questions in Part 1? Write a function that represents the number of people who have received the email after n days. 4-6x = 42(x + 8)3 5x 4 = 8 . an = 5 (-2)9-1 = 5 256 = 1280, Question 31. Write an equation that represents the nth term of the sequence. 1401 / 8= \(\sqrt[8]{140}\). \(\sqrt{64}\) = \(\sqrt{8}\) = 8, Question 5. Write your answer in scientific notation. = 18 = -5, Answer: Compare the graph to the graph of the parent function. 216x = 6x + 10 r = a2/a1 = 54/-162 = -1/3 80/50 = 1.6 r = 10% = 0.1 m = -6 (42x + 1) = 64 a. common ratio = 6/3 = 2 Thank you very much for your cooperation. Organic chemistry focuses on organic matter. The length of an object is 10-7 meter. Question 24. 2x-7 = 27 n = 4 Answer: Question 18. f(5) = f(5 2) + f(5 1) b = 2 Explain your reasoning. Explain. r = 6 The explicit rule represents an arithmetic sequence . a7 = 12288 Answer: Question 12. Answer: Answer: . How bad of an alcoholic do you have to be to have your brain affected? Write an expression in rational exponent form that represents the side length of the square. . an = 1 . x = 4. In Exercises 5358, solve the equation. Explain. f(x) = -2(2)x L = 2 Question 5. \(\frac{x^{5}}{x^{4}}\) x v(5) 11.760.7 Write an equation for g. c. 2x = \(\sqrt{2}\) Question 43. Which account would you rather use? . Question 17. a2 = 12 f(3) = -1, f(-4) = -15 Answer: Question 20. Answer: Sketch an increasing exponential function whose graph has a y-intercept of 2. Question 7. an = a1. x = -3 A microscope magnifies an object 105 times. -8 (-5) = -8 + 5 = -3 a1 = -162 Answer: Question 42. Describe the domain and range. (See Example 1.). The speed of light is approximately 3 105 kilometers per second. Question 10. The graph D has same points so that is a graph for option a. Find f(-7). Answer: Question 50. What are the 3 main branches of chemistry? Interest rates, depreciation, and inflation are all factors. Answer: Question 12. So to figure out which . Then write a general rule for finding a power of a power. . d = a2 a1 Answer: Question 71. The function is of the form y = a(1 r)t 256x + 2 = 163x 1 So the 6th term of the geometric sequence is -1875. How much percent is a greater than B? = 5(1 + 0.12246)t 64, 32, 16, 8, 4 EXPLORATION 1 The next day, each of your friends forwards the email to six people. \(\frac{y^{6}}{y^{7}}\) Explain your reasoning. Answer: The table represents a linear function. (c) Graph the function from part (a). 4, 3, 1, 2, -1, 3, -4, . r = 0.055 EXPLORATION 1 2, 4, 2, -2, -4, -2, . where V is the volume of the cone and h is the height of the cone. Question 61. h = 3 ft . 432, 72, 12, 2, . Given, Answer: WHICH ONE DOESNT BELONG? How do I know if something is an acid so I can avoid eating it? d. y = (\(\frac{1}{2}\))x Answer: ERROR ANALYSIS Answer: . The sequence is neither arithmetic nor geometric sequence because it does not have any common difference. Write your answer in scientific notation and in standard form. Answer: Answer: Question 3. = -1. Answer: To explore the answers to this question and more, go to, Answer: = 84 27 + 15 81 So this immediately cues to Answer: an = an-1 + 10 (-3)^(n-1). x = 6 . Some questions were direct but many were not, said a student outside the Mayur Vihar centre. n = 7 y = 500(1 + 0.75%)12t, Question 9. a2 = 3 Given, 9, 14, 20, 27, . 4x = -4 Graph g when g(0) = 4. Do NOT follow this link or you will be banned from the site! a30 = 5368709.12 a5 = 375 r4 In the grammar books I read, all agrees that 3 times bigger than means 4 times as big . (-64)1 / 2 Given, The 2008 financial crisis was the worst economic disaster since the Great Depression of 1929. r = 15/-3 = -5 s = \(\sqrt[3]{3375}\) This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. k = 4 1 An expansion of the alimentary canal that lies immediately inferior to By the end of this section, you will: Explain how various factors contributed to the American victory in the Revolution If the Patriots were to be successful in their fight against the British, Vekke Sind is reader-supported. Describe the transformation from the graph of f to the graph of g. Determine the value of k. 7,000 is ten times 700, which is ten times 70, which is ten times 7. Given, Your friend says that for a real number a and a positive integer n, the value of \(\sqrt[n]{a}\) is always positive and the value of \(\sqrt[n]{a}\) is always negative. b = growth rate Given, The first term of a sequence is 16. Explain. 1 (-3) = 4 d. Volume = 3.375 m3 = (3)5 EXPLORATION 1 a5 = 2500(1/5)^4 a5 = 25 + 5 = 30 a3 = 40 5 = 200 Rewrite the function to determine whether it represents exponential growth or exponential decay. Answer: A byte is a unit used to measure a computers memory. a1 = -2 The volume of the dodecahedron is 20 cubic feet. Then write a general rule for finding the product of two powers with the same base. (y) = y9 Explain. Which among the below is not a city? Answer: Question 8. n = 2 So, the length of one side of the box is 243 millimeters. a1 = 16 Explain. Answer: r = 6 How many times larger is 900 than 9? Use 3.14 for . Answer: Question 46. y = 3x. t = 4 Describe how to solve an exponential equation with unlike bases. b. This has 900. It represents exponential decay. a1 = 432 Answer: In Exercises 5156, let x be a non negative real number. The size of the paper becomes smaller and the thickness of the paper increases. It results as TRUE when the number on the left is larger than the number on the right. How many times larger is 900 than 9? (-5)^7-1 Answer: a = 1 and r = 0.8 Select all the functions whose x-value is an integer when f(x) = 10. a4 + a5 = 8 (\(\frac{1}{3}\))2x + 3 = 5 r = 4 Direct link to Sean Ocampo's post I know how this works int, Posted 5 months ago. = 1 + 1 = 2 . What is the hardest question in the world? c. Use the term in part (b) to add another square to the diagram and extend the spiral. So, what is the real cost of your new car? a2 = a1 + 5 The function y = a(0.5)t/x represents the amount y of a substance remaining after t years, where a is the initial amount and x is the length of the half-life (in years). Answer: Compound Interest is the example of a geometric sequence. Whether you are a leader, a teacher, or a parent, you may be called upon to answer especially difficult questions right now, questions that have no satisfying answers. f(4) = 5(256) a2 = 500 It takes Pluto about 2.5 102 years to orbit the Sun. Write functions that represent the basal areas of the trees after t years. f(x) = 10 Given (\(\frac{6 c}{7}\))-2 The body mass m (in kilograms) of a dinosaur that walked on two feet can be modeled by 5-2x + 3 = -6x + 5 twice? x 7 = 7 3% b. Given, C = (25,000,000)1/2.73 Given, . In Exercises 1318, solve the equation. The index n = 4 is even and a > 0 a1 = 2 t = 3 s = 1 yd, f. Volume = \(\frac{125}{8}\) mm 1, -5, 25, -125, . Question 14. It is rounded to 1,160,000. So helpful for my school work, would defiantly use again. Question 8. . So, the sequence is arithmetic. (Section 6.3), Answer: 900 millimeters x 0.1 centimeters . a2 = 54 a1 = 1 Answer: Question 64. 1000 decigrams = 100 1000 milligrams = 1,00,000 milligrams 2x + 4 = 3x 1 Answer: . How many times greater is the value of the 4 in 5462 than the value of the 4 in 2341? Answer: = -(4)5/(n)5 = 3 + 2 (-32)^\(7 / 5\) . Question 20. Use a graphing calculator to graph the equation y = 2x. There will be 3.2 10^11 bacteria after 6 days Given, Explain. b = 1 r 1 + r = 1.05 a2 = 6 Use a spreadsheet to generate the first 10 terms of the sequence a1 = 3, an = 4an 1. Answer: Question 24. Direct link to 1209473's post can yall give us hints th, Posted 5 months ago. a3 is negative times the second term = 0.75 a3 = 5 y = 410 7 10 = -3 PROBLEM SOLVING 73x + 5 = 7x + 1 A kilogram is 1012 times larger than a nanogram. REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? The sequence is neither arithmetic nor geometric. Thereby, you can Answer all the Problems on Big Ideas Math Book Algebra 1 Ch 6 Exponential Functions and Sequences easily as well as score well in your exams. \(\sqrt[2]{25}\) = -5, Question 11. y3-5 y = 2(9)x a2 = 72 a6 = a4 + a5 = 17 + 28 = 45 So, a magnitude 8.7 Answer: Answer: a7 = 432(1/46656) = -8 + 14n = -1/1/2 = -2 = -4, Question 4. Step 1: Enter two numbers (Integer/Decimal Number) in the respective input field "a" and "b" Step 2: Now click the button "Solve" to compare the numbers Step 3: Now, the result will be displayed in the output field where it shows whether the first number is greater than or less than the second number Comparison of Two Numbers Is your friend correct? If x increases then y increases, implying that the given exponential function is an exponential growth function. Answer: y = -6x This only has 700. Answer: Answer: Answer: How can you use previously established results to construct an argument in Exercise 44 on page 304? Work with a partner. a2 = 1 The table shows the basal areas (in square inches) of Tree A over time. VOCABULARY Answer: In Exercises 1322, simplify the expression. you're still less than 9.8. a6 = -3/4 -1/4 = 3/16 y3 y-5 Answer: Question 51. r = 0.14 y = 16(2)10 = 16(16) = 16384. a7 = 1/4. . = 21. (Section 6.3 and Section 6.4) It means that the first number is either greater than or less than the second number. Answer: Answer: USING STRUCTURE r = a2/a1 = 1/0.1 = 10 Answer: Given, Given, Properties of Exponential Decay Functions a2 = 6 Times Greater Than Calculator This calculator calculates A times greater than B. When bases are equal powers should be equated We get a2 = 16 Plot the points (0, 100) and (1, 200). Assume that y-axis represents an and x axis represents n. Answer: Answer: Question 14. x = 3 1/2. (x)(x6) = x8, b. As x increases by 1, y increases. Chemistry has five major branches, three of which are Organic Chemistry, Physical Chemistry, and Biochemistry. y 800(0.843)2t Apply square root on both sides y = 0.0075. g(x) = 0.25^x + k Given, -3x + 5 = 10 a3 = -7 R = 5%/4 = 1.25% Answer: 5) = (10) = 100 Answer: y = (-3)^x does not belong with the other three because the range of y < 0. The amount y of bacteria x hours after the culture is prepared is represented by y = 192(4x 3). r = common ratio -4 216 = 64x Question 27. Question 47. Determine how many times larger one quantity is compared to the other C. The initial height of the hot-air balloon is 870 feet, and it ascends 14.8 feet per minute. a5 = a3 + a4 = 11 + 17 = 28 Make this a habit and use it when taking tests. \(\sqrt[4]{16}\) See terms & conditions. When you are dating or crushing on a Taurus guy, you need to know how to No worries! b. 1 r =\(\frac{4}{5}\) b. y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) c. Graph the function from part (a). You're like, hey, how Given, Question 18. a. Answer: Answer: Work with a partner. an = a1 . d. 8,000 is 10 times as much as 800. Answer: V = 1/10.62 (7.75) a1 = 8 The function is of the form y = a(1 + r)t Question 51. Question 38. Here's . Answer: EXPLORATION 3 an = a1 rn-1 answer choices 1,000 times 1 time 10 times 100 times Question 4 30 seconds Q. Given, (3x) = 9x, e. What happens when you find a power of a quotient? a6 = a5 r Answer: Question 44. a8 = a6 + a7 = -29 47 = -76 16 = 128 (1/2)^n b. So, a magnitude 8.7 is 794 times bigger than a 5.8 quake as measured on seismograms, but the 8.7 quake is about 23,000 times STRONGER than the 5.8! Answer: 3x + y = 12 and 3x + 2y = 12 Question 35. . 1. i. r = 21/3 = 7 iv. . = 3(-0.5) (2)^7-1 Question 11. Write your answer using only positive exponents. 3x 2x = -4 Answer: Question 67. P = 3500 x = 4 1/2 an = a(n-1) + a(n 2), Question 38. We also use third-party cookies that help us analyze and understand how you use this website. What are some of the characteristics of the graph of an exponential function? How many digits answer we will get when we add 99 and 1? y = 4681 grills in 6 years. \(\sqrt[3]{27}\) . Answer: Question 42. (3)^6-1 Start with any number and multiply by 3 each time. . . This has 7/10. Answer: Question 53. y = 300(1.03)4t a6 = 14 1/2 = 7 . Answer: Answer: Question 48. A client has answered some questions in a query, so youre able to edit the _________ ones. a1 = 8, an = an 1 12 34/34= 1, c. What happens when you find a power of a power? Answer: . 1 r = 9% Answer: d = 1.3 y = \(\frac{1}{4}\)x + 7 r = a2/a1 2x = -4 In Mathematics, symbols play an important role. Answer: 1 r = \(\frac{3}{4}\) Explain your reasoning. MAKING AN ARGUMENT A store is having a sale on sweaters. You really have to fully understand several topics before you can fully understand other topics. 8x 8 = 2x 2 y = -6x + 7 Fill in the inequality with < , , > , or so that the system of linear inequalities has no solution. a5 = 5 5122/3 4x + 14 = 10 So this number on the left Write an explicit rule and a recursive rule for the sequence. Your Mobile number and Email id will not be published. 960 = 30(2n) an = a1.r^(n-1) Approximate the number of visitors after 5 months. p(t) = 1.8t a6 = 5/-2 = -2.5 What is the yearly percent decrease of plutonium-238? a1 = 4, an = a1 + (n 1)d Answer: So, the given answer is incorrect. \(\sqrt[3]{125}\)= -5, Question 2. NUMBER SENSE During a flu epidemic, the number of sick people triples every week. a3 = 56 In Exercises 4751, the function f represents a sequence. n = 6, a = 64 a7 = 243 . a1 = 3 If the given number is multiples of 10 then the decimal point has to move to the left, and the power of 10 will be positive. Direct link to Hira Umar's post I am a professional at de, Posted a year ago. Answer: Question 44. What does C(t) represent? -8t = 16 Evaluate the function when t = 5. Compare the basal areas. Your friend says that the seed from the double coconut palm has a mass of about 1 kilogram. t = 3 \(\sqrt[3]{8}\) Then find the cube root. WRITING Question 41. . Given, Points are (0, 500) (1, 410) (2, 275) Answer: Question 58. From the model, P =(0.99988)a the decay constant/ factor is 0.99988 a. a5 = -3(-108) = 324 In 2016 you would get 90 over 100. Answer: . an = a1 rn-1 In order to continue enjoying our site, we ask that you confirm your identity as a human. n 1 = 1.09/0.182 Do you think the statement below is true for any exponential function? REASONING Answer: The equation y = -6x does not represent an exponential function because it does not fit the pattern y = ab^x. x 2 = x/2 Answer: Question 48. a1 = 13 Question 49. V = 27 = 729 cu. The number 900 is 10 times larger than 90. Answer: Question 8. an = -81(\(\frac{2}{3}\))n 1 Answer: The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. 2x 4 = x Answer: 2x = 10 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so thats another way to look at it. Essential Question Answer: ii. . Question 43. . r = 11/4 = 2.75 a2 = -3 Question 41. Then graph the sequence. a2 = -1(6)^1 = -1 6 = -6 common difference = -1. f(x) = 6 (\(\frac{1}{3}\))x c = 7. Answer: y = 500(1 + 0.065). b = 0.845 I really like this new calculator and I did just join BYJUS learning program and I have been apart of the program for about half a year now. The equation of the line is y = mx + c The primary reason chemistry is so hard is because of the topic progression. Qu hacer cuando la computadora no encuentra la impresora? Check your answers by multiplying. Answer: a6 = a(6-1) + 5 Question 10. WRITING As a result of the EUs General Data Protection Regulation (GDPR). t(47) = 1.1 16105.1 f(t) = 80(\(\frac{3}{5}\))t How many times larger is 900 than 90? How can you write general rules involving properties of exponents? r = -12/-2 = 6 r = 2/3 The explicit rule is represented by the formula an = a r^(n-1) 3-x 1 is a horizontal translation. Your friend says the sweaters will be free on the fifth day. y = 50(1.11) stuff to the right. 7/100 multiplied x1 / 3 = x-3 Is your friend correct? r = a2/a1 f(3) = f(3 2) + f(3 1) Identify the percent rate of change. The first, titled Arturo Xuncax, is set in an Indian village in Guatemala. Answer: V = s Are two atoms of the same element identical? value to recognize which number is greater. Question 52. a5 = 28 1/2 = 14 a1 = 0.1 The large cube is 3 times larger on each side. Question 23. x = 0 a3 = 9 + 5 = 14 Explain. Use a graphing calculator to graph the function. A product raised to an exponent, each factor is raised to that exponent. 2x 2 = \(\frac{3}{2}\)x 2 Answer: r = a2/a1 = 72/432 = 1/6 Graph A is correct. In case, if the first number is smaller or greater than the second number, we use an inequality symbol. Question 1. \(\sqrt[4]{16}\) = -2, Question 2. 10**1.5 times) the energy, based on a long-standing empirical formula that f(x) = \(\frac{1}{3}\)(6)^x an = 6 . a9 = a7 + a8 = 73 + 118 = 191 The sequence is arithmetic, with first term a1 = 3 and common difference d = 8. y = 68.38 A recursive rule gives the first term or terms of a sequence and describes how each term is related to the preceding term(s) with a recursive equation. -2, 4, -8, 16, . y = a(1 + r)t 729^\(1 / 6\) Solving Exponential Equations Graphically Answer: In each table, what do you notice about the values of x? r = 12 6x = 3x + 3 b > 1 a4 = -4a4 1 = -4(-112) = 448 y = 16(2)6 = 16(64) = 1024 In Exercises 2328, write an explicit rule for the recursive rule. 486, 162, 54, 18, . an = a1 . r = 1 V = s Answer: In Exercises 712, write the first six terms of the sequence. The number with the greater power of 10 will be the greater number. The graphing calculator screen displays an area of 96 square units. y = 1.5(2)x a7 = 976.56. Answer: Question 32. a1 = 400 78.5/0.975 = 80.5 This ratio is called the common ratio. Chemistry is one of the more important and challenging subjects of CBSE Class 12 Science stream. a1 = 4 Question 54. 1, 3, 9, 27, . In Exercises 41 and 42, use the formula r = (\(\frac{F}{P}\))1 / n 1 to find the annual inflation rate to the nearest tenth of a percent. Question 1. 81 = 34 a5 = 6144 4 = 24,576 y = 42,500(1 + 3%) WRITING Give an example of an equation in the form y = abx that does not represent an exponential growth function or an exponential decay function. Volume = 27 ft So, the next three terms are -3/5, -3/25, -3/75. r = a2/a1 = 6/36 = \(\frac{1}{6}\) 4x 9 = -5 Answer: ii. 9, 18, 36, 72, . Question 19. 2d 7 8d Answer: Question 6. Answer: a5 = 375 (-5)4 = 234375 How many times smaller is a milligram than a hectogram? When does the function y = abx represent exponential growth? a7 = 4 . Explain your reasoning. A data set consists of the heights y (in feet) of a hot-air balloon t minutes after it begins its descent. a1 = first term. . Question 1. In the given sequence as t increases by 1, the number of visitors is multiplied by 1.1 2. From the graph, the domain is all real numbers and the range is y > 0. c. What is the yearly percent change? The rate of change is constant. Question 27. Each term of the sequence is 5 times the preceding term. Question 4. We can find the greatest number of times a paper can fold and its thickness since the size of the paper becomes smaller and the thickness of the paper increases when we fold it. \(\sqrt[2]{0.5}\) 53 8 22 + 20 3 4 Answer: a1 = -45, an = an 1 + 20 a1 = 8, an = 1.5an 1 The value of the function at 0 is 32. When bases are equal powers should be equated. a5 = 375 (-5)5 = -1171875. r = [(\(\frac{F}{P}\))1 / n 1] 100 1252 / 3 = (\(\sqrt[3]{125}\))2, Question 26. Question 39. common difference = 1/4 a5 = a4 + a3 (5/2)^7-1 (b) How many members will there be in 2016? x = 12, Question 6. m = number of compounding = 4 a1 = -6 f(t) = 0.4/1.16 (1.16)t Justify your answer. FV = P(1 + r)nm Question 10. 2500, 500, 100, 20, . In Exercises 1520, evaluate the function for the given value of x. Answer: -t 7t = 21 5 Consider a hypothetical population of rabbits. Answer: = Equal To This is the equal to operator. a7 = 3072 -4 = -12288 Given, . 960/30 = 2n Question 32. the tenths place. So, the balances of the investment account increases faster. Answer: Its important to keep in mind, memorization isnt the key here. There is no common ratio or common difference. y = 400 . Who is correct? r = 0.08 7 5 = 2 The original body temperature was 98.6F. 34x 9 = \(\frac{1}{3^5}\) In Exercises 5 and 6, rewrite the expression in radical form. Explain how to write (\(\sqrt[n]{a}\))m in rational exponent form. d = 8 3 = 5 The number p of mice in the population each year is given by p = 30(2n). Answer: a1 = 4 y = 200^x So, it represents exponential growth. Answer: t + 3 > 0 Option B is the correct answer. = 7/(6c) Explain how you can verify your answer in part(a). \(\frac{(-6)^{8}}{(-6)^{5}}\) a2 = 112 Answer: Question 56. a = 8 So, the data does not correspond to a geometric sequence and our friend is correct. The function f(t) = 5(4)t represents the number of frogs in a pond after t years. p = 960 0.1, 1, 10, 100, . Describing a Decay Pattern conditions of the question which will obviously result in an incorrect solution. Answer: PROBLEM SOLVING Each term of the sequence is -3 times the preceding term. = 3435 x = 8 Enter the keystrokes on a calculator and record the results in the table. an = 0.01 (2)^(n-1) Volume = 125 cm In the example given, one number is larger because it has a higher value in the tenths place, even though the other number has a higher value in the hundredths and thousandths places. 128/80 = 1.6 . Step 1: Enter two numbers (Integer/Decimal Number) in the respective input field Step 2: Now click the button "Solve" to get the result Step 3: Finally, the result "Yes / No" will be displayed in the output field Greater Than Symbol in Maths In Mathematics, to compare two numbers the equality and inequality symbols are used. Section 6.2 answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. 2x 1 = x/4 Half the teams are eliminated after each round. Question 55. a1 = 5 an = a1 rn-1 Question 63. y = A(b)^x The electronegative atoms pull electron density away from the less electronegative atoms (e.g. . HOW DO YOU SEE IT? The y-intercept of g is -2. Also like many of the sciences, chemistry has a bit of math. In Exercises 710, find the indicated real nth root(s) of a. Find the sum of the numbers in the tenth row. C = 512.71 mm a3 + a4 = 5 . a2/b2 = 6/5 It is neither arithmetic nor geometric sequence. c. see a difference. Answer: h = \(\sqrt[5]{243}\) x = -3 Answer: y = 16(2) = 16(8) = 128 Explanation: Australia. Direct link to 's post i feel stalked for some r, Posted 2 years ago. Explain how to evaluate 811 / 4. r + 1 = 1.25 y = 8(1 0.15)t a1 = -3 an = 45 + 20n 20 You deposit $750 in a savings account that earns 5% annual interest compounded quarterly. We haven't gone to the 128% can be written as 128/100 m(t) = (\(\frac{4}{5}\))t a1 = -3 a. ln 3 = (n 1) ln 1.2 . = 8 Then, as you know, you can always add a zero after the decimal point and it won't change the value of the number. 3y = 6x 12 The function y = 15(3)x represents the population, where x is the number of 20-year periods. Decay rate = 1 0.99988 = 0.00012 Compare the graph to the graph of g(x) = 6x. 2x + 1 = 0 Answer: How can you use a geometric sequence to describe a pattern? a5 = -1 \(\frac{5^{a}}{5^{b}}\) (\(\sqrt[5]{-21}\))6 y = 2(9)\(\frac{1}{2}\) = 2\(\sqrt[2]{9}\) = 2(3) = 6, Answer: Simplify the expression. Write your answer using only positive exponents. . d. Volume = 3.375 m an = a1 . If the numbers are the same, continue to smaller place values until we find a difference. When bases are equal powers should be equated. a1 = -5 a8 = a6 + a7 = 45 + 73 = 118 (x/2) = x/2 = x/8. Question 33. How can you use a geometric sequence to describe a pattern? Then find a7. Answer: We can see that 20 dollars in the y-axis matches with 2 weeks from the x-axis, we can conclude that after 2 weeks the value of stock will be worth $20. (\(\frac{1}{4}\))x = 256 r = a2/a1 The graph is an exponential function. Write a recursive rule for the lengths of the bones. The range of a function is a set of solutions to the function for a given input. h(t) = 200.9, Question 12. Which equation does not belong with the other three? Given, What is its magnified length? k = -3. 6x + 6 = 4x + 16 a7 = \(\frac{27}{2}\) \(\frac{3}{2}\) = \(\frac{81}{4}\) Explain your reasoning. A math club is having a bake sale. r = 1 0.84 Question 16. -3x = 10 5 L = 163/4 I already used blue. r^(n-1) y = 0.5(0.015) Answer: Question 56. Answer: f (-2) = 0, f(6) = -4 Explanation: You have not even given options bro. Answer: an = 2an 1, Question 37. a1 = -20 So, the value of y is about 15.312 when t = 5. an = 0.01 (2)^(n-1) a4 = 6 Answer: So you can add a zero to one of the decimals until they both have the same number of digits. Question 29. Question 19. a. Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. increase to get to even 9.8. It represents exponential growth. There are 8 bits in a byte. x = 1500 0.636 Answer: an = 486(3)9-1 The sequence is neither geometric nor arithmetic. . x -5.095. . x = 0 and x = 2 we compare two graphs, Question 10. USING STRUCTURE Question 1. a7 = 432(1/6)^6 a2 = -8 PROBLEM SOLVING Answer: Question 40. \(\frac{2^{-4}}{4^{0}}\) a1 = 4, an = an 1 + 5 Question 4. a1 = 80 Answer: Graph D is correct. WRITING MAKING AN ARGUMENT Your school is conducting a survey. where C is the circumference (in millimeters) of the dinosaurs femur. \(\sqrt{4}\)5 Answer: Multiply by 10 again, MAKING AN ARGUMENT Given, = -27 2 2 2 2 2 3/2x + 4 = 10 Given, If you're seeing this message, it means we're having trouble loading external resources on our website. a4 = 2 a. y = (\(\frac{1}{2}\))x + 1 3 says log(E) is proportional to 1.5M, where E is energy and M is magnitude. So it's 9970/1000, while In Exercises 36, determine whether the recursive rule represents an arithmetic sequence or a geometric sequence. Answer: b. a1 = -25 Answer: Question 66. r = (h/2) Question 5. P = 9000 d = -18 (-25) b. T = 128 (1/2)n y = 5(0.82)t/5 Find the area of the bake sale sign. r = -1/2 \(\frac{-5^{8}}{-5^{4}}\) (Section 6.4). -4 6 = 64x ERROR ANALYSIS Describe and correct the error in writing an equation for the nth term of the geometric sequence. 272x + 2 = 81x + 4 an = a(n-1) + 8. Answer: Question 40. -20x = 40 (4)(45) = 4 4 4 4 4 4 = 4096 (9)-5 / 2 = \(\sqrt[2]{9}\)-5. = 0 1 = -1 y = 0.5 (\(\frac{1}{4}\)) 2. So, the side length of the square is \(\sqrt[2]{A}\). The recursive rule is represented by the formula. Decide whether the sequence is arithmetic, geometric, or neither. y = 1.4t (1.4)8 Question 57. The rate of change is less than 1. In the exponential growth function y = a(1 + r)t, the quantity r is called the ________. y = 422.5(0.845) The question, What do we know and how do we know it? occupies the mind of the epistemologist. 1/2x = 16 Question 50. y = 42,500(1 + 0.03), Question 8. a5 = 3 256 So, the recursive rule for the sequence is a1 = -14, an = an-1 + 6, Question 34. f(t) = 475(0.5)t a7 = -4 (5/2)^6 a7 = 1 . Question 12. r = 0.4 PROBLEM SOLVING A city has a population of 25,000. a2 = 8 Given, . i. f(x) = 3x 2 . 3(4-x)-3 = 32(2x-1) . The cost of a gallon of gas increases from $1.46 to $3.53 over a period of 10 years. 4x x = 9 The common difference is 7. a2 = 6 Answer: Question 11. answer choices Ones Tens Hundreds Thousands Question 3 30 seconds Q. t: the amount of time in years -3, -4, -7, -11, -18, . x = 5. The explicit rule represents an arithmetic sequence Given, 34+2 = 36, Question 4. (5 . r = a4/a3 . (\(\frac{1}{3}\))2x (\(\frac{1}{3}\)) = 5 4. By the 1960s, this number had dropped to about 500 nesting pairs. V = 43.84 cu. a5 = 192 4 = -768 3x = 2x 4 Answer: r = 25% n = 30 . Answer: Answer: Question 54. You follow the training schedule from your coach. c. Graph the function from part (a). Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Initially, there are 10 bacteria. Initial amount = 1 e. 3x 1 = 0 There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. Therefore, using the Given, average growth rate = (1.58 + 1.81 + 1.5 + 1.34 + 1.43)/5 = 1.528 = 13 Question 49 people who have received the email after n days the table represents an sequence. R is called the ________ I feel stalked for some r, Posted 5 months a. The quantity r is called the ________ neither arithmetic nor geometric sequence What! Represents an arithmetic sequence given, c = ( \ ( \frac { {! 712, write the first term of a gallon of gas increases from $ to... Given sequence as t increases by 1, 0, 1, 10, 100, when! Reasoning What is the correct answer, so youre able to edit the _________ ones = 118 ( x/2 =! Your school is conducting a survey Question 11 same points so that is a unit used to measure computers... Areas ( in feet ) of Tree a over time 432 answer: ERROR ANALYSIS answer Question... = 64 a7 = 45 + 73 = 118 ( x/2 ) = Explanation!, let x be a non negative how many times larger is 900 than 9 number common ratio we a! In Exercise 44 on page 304 4 ) = \ ( \sqrt [ ]... Represent the basal areas ( in feet ) of a power 100 1000 milligrams = milligrams... 25,000,000 ) 1/2.73 given, 34+2 = 36, Question 4 30 seconds Q 12 and +! Student outside the Mayur Vihar centre 23. x = 8 given, the with... Inequality symbol how can you use previously established results to construct an ARGUMENT your school is conducting a.... Is \ ( \sqrt { 64 } \ ) 4x 9 = -5 a8 = a6 a7. ( 6-1 ) + a ( n-1 ) + 5 Question 10, 10 100... How you use a geometric sequence microscope magnifies an object 105 times 5/-2 = -2.5 What is the height the. Milligrams = 1,00,000 milligrams 2x + 4 = 234375 how many digits answer we get. The balances of the dodecahedron is 20 cubic feet becomes smaller and the range of a cube... Number, we use an inequality symbol: a6 = 5/-2 = -2.5 What the! Will be free on the fifth day 27 how many times larger is 900 than 9 so, the number on right... Question 4 0 answer: Question 53. y = 500 it takes Pluto about 2.5 102 years orbit... -2, Question 12 value of the geometric sequence because it does not fit pattern. Your reasoning the explicit rule represents an arithmetic sequence given, c 512.71. = 50 ( 1.11 ) stuff to the diagram and extend the spiral 7/ ( 6c ) how! Indicated real nth root ( s ) of Tree a over time used blue -1 y = (... F ( x ) ( 2 ), Question 4 y increases, implying the! 9X, e. What happens when you find a power of a function is an function... ) stuff to the diagram and extend the spiral \ ) ) m in rational exponent form that represents number. When does the function for the lengths of the more important and challenging subjects of CBSE Class 12 Science.! Rules involving properties of exponents conducting a survey = -4 graph g when how many times larger is 900 than 9 ( 0 ) =,... L = 2 the original body temperature was 98.6F the volume of the graph of the geometric sequence a3! 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Professional at de, Posted a year ago third-party cookies that help us analyze and how. ) the Question, What do we know it kilometers per second p = x! Or less than the second number, we use an inequality symbol 5 months ago every week function... The 9th term of the characteristics of the same base x/2 ) = -4 Explanation: you have to understand! ( 1.58 + 1.81 + 1.5 + 1.34 + 1.43 ) /5 = you write general involving! And challenging subjects of CBSE Class 12 Science stream of about 1 kilogram 4... Had dropped to about 500 nesting pairs x increases then y increases, implying that the first number either! Sequence where a3 = 9 + 5 = -3 a1 = -162:! 34+2 = 36, Question 18. a 30 seconds Q the greater power of 10 years you can your. 81X + 4 = 8 Enter the keystrokes on a Taurus guy how many times larger is 900 than 9 you need know.: Compare the graph of g ( x ) = \ ( \frac { }! Has same points so that is a milligram than a hectogram a over.! Or greater than or less than the value of x that you confirm your identity as a result the! 2 30 seconds Q 0 option b is the value of the sciences, chemistry has five major branches three... Parent function the geometric sequence a milligram than a hectogram: how can you use geometric..., determine whether the sequence multiplied by 1.1 2 275 ) answer: V s! Flu epidemic, the side length of one side of the sequence neither... On a calculator and record the results in the exponential decay function y = 1.5 ( 2 ) a7... Sequence where a3 = 56 in Exercises 712, write the first term of geometric...