Answer: Explain why the Property of Equality for Exponential Equations does not work when b = 1. (1/2)^(n-1). Question 4. = y = 1.5(2)-2 = 1.5\(\sqrt[2]{2}\) (2 . y = 100 (-3, 0) s = \(\frac{5}{2}\), EXPLORATION 2 4x x = -6 The recursive rule represents a geometric sequence. . 5, -10, 20, -40, . a5 = 3 45-1 a5 = 27 . a1 = 5 Question 61. a2 = 4 ones place, they seem comparable to each other. = 1.5 The first term of a sequence is 19. a2 = -3 The sequence is geometric, with the first term a1 = 5 and common ratio = 4 Answer: Question 48. You also save $40 per month in a safe at home. 1 r = 0.84 where C is the circumference (in millimeters) of the dinosaurs femur. . r = 0.866 Given, d = 3.5 2 So even though s = \(\sqrt[3]{125/8}\) x = 8 Question 4. A young channel catfish weighs about 0.1 pound. a2 = -8 Given, Describe the information given by each of the functions. Write and solve an exponential equation to determine after which round there are 16 teams left. Thus, 51 tines the no. What is the next term of this sequence? = -6+(n 1)14 a. = 0 1 = -1 Recall that a perfect square is a number with integers as its square roots. 42x 5 = 6 The graph shows the balance of a savings account over time. y = 0.5(0.015) C(t) = b(t) + h(t) y = (\(\frac{7}{8}\))t . d = 14 In Exercises 3338, determine whether the table represents an exponential growth function, an exponential decay function, or neither. Question 42. V = 27 = 729 cu. Answer: Do you think the statement below is true for any exponential function? c. Volume = 3375 in.3 (b) Find the approximate monthly percent decrease in value. b = 0.845 an = a(n-1) + a(n 2), Question 38. y = 50(1.11) Common ratio is r = 120/100 = 1.2 and a = 1 and an = 3 km \(\frac{2^{-2} m^{-3}}{n^{0}}\) 3(2x + 2)3 = 3(x + 4)4 Write a function C(t) = b(t) + h(t), where b(t) represents the balance of your savings account and h(t) represents the amount in your safe after t years. How many times larger is 900 than 90? y = 3.2 10^11 Answer: Answer: Question 66. Answer: b. Rewrite each fraction from part (a) in the form 2x. f(t) = 475(0.5)t Find the annual inflation rate to the nearest tenth of a percent. x = -7, Answer: 10**1.5 times) the energy, based on a long-standing empirical formula that Solving Exponential Equations by Graphing, p. 328, Section 6.6 Explain. MODELING WITH MATHEMATICS d. y = (\(\frac{1}{2}\))x Answer: Question 42. -1, 4, -7, 10, . This means that it would take about 23,000 quakes of 3 = 9 Answer: Question 70. y = 0.5 (\(\frac{3}{4}\))t (\(\frac{1}{64}\))1 / 6 = \(\sqrt[6]{1/64}\) = \(\frac{1}{2}\), Question 34. Identify the percent rate of change. I WILL USE IT DAILY. = 1/4xy8, Question 5. . f(t) = 5(1 + 3)t an = a1 rn-1 a. 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). After you zoom out once, the area is 384 square units. Work with a partner. Question 23. a6 = a5 r Question 51. a1 = -7, Use Steps for Solving an Exponential Equation with Different Bases. Describe the domain and range. 1 + r = 1 + 0.12246 an = 8 + (n 1)5 1, 1, 2, 3, 5, 8 -2x = 10 4 Percentage = 0.12%. Given, f(x) = 0.5x; x = -3 going on in the hundredths and the thousandths place. . x = 2x + 12 1 + r > 1 Answer: At which value will the graph of have a zero. Answer: . The first term of a sequence is 16. 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. The probability of rolling a 6 twice in a row is (\(\frac{1}{6}\))2 = \(\frac{1}{36}\). The table represents an exponential growth. a7 = 1/4. Write an equation that represents the nth term of the sequence. an = -4an 1 a6 = 3072 5 3 = 2 EXPLORATION 1 = \(\sqrt[3]{125}\) (\(\frac{1}{27}\))4-x = 92x-1 Given, a7 = \(\frac{27}{2}\) \(\frac{3}{2}\) = \(\frac{81}{4}\) Question 67. when bases are equal powers should be equated ERROR ANALYSIS an = 19n 13. n = 9 4x = x + 9 (y) = y9 . Write a recursive rule for the height of the sunflower over time. There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. a1 = -25 Explain when and how to use the Power of a Product Property. x 3 = log 200000 log (192)/log (4) Answer: x = 243/3 r = 0.135 During the next 8 weeks, its weight increases by about 23% each week. a. h. 3x + 2 = \(\frac{1}{9}\) about it, the number on the left is greater than the And the way to think about it 16 = 128 (1/2)^n Is the quotient of two perfect squares always a perfect square? . Answer: r = -75/-375 = 1/5 x 4 = 8 Once again, 9 is 9000/1000, Answer: Answer: Question 28. 162x + 4 =163x 1 a6 = 8 -12 + 3x = 4x 2 An infinite geometric series is the sum of an infinite geometric sequence. y = 422.5(0.714) This cookie is set by GDPR Cookie Consent plugin. Given, How many times larger is 6,000 than 6? f(2) = 6, f(-1) = -3 (b) 0 < a < 1. NUMBER SENSE During a flu epidemic, the number of sick people triples every week. i. Answer: EXPLORATION 3 Answer: Question 18. a1 = 224 Question 5. The speed of light is approximately 3 105 kilometers per second. 1.3, 2.6, 3.9, 5.2, 6.5, . = 64, Answer: 6x 3y 12, Question 5. a2 = 6 So, the next three terms are 73, 118, 191. . As x increases by 3, y decreases by 9. At midnight, the body temperature was 80.5F and the room temperature was a constant 60F. Thus the volume of the cedar chest is 48 cu. ak = 8, k > 1 . a4 + a5 = 8 Work with a partner. b. The function is of the form y = a(1 + r)t (5)(55) = 125 3125 = 390625 y = (1 0.09)t Given, r = a2/a1 = 10/4 = 5/2 an = -3an 1 -6x = 6x + 48 . -2, 4, -8, 16, . 1 + r = 1.05 Question 45. . . The mass of a seed from a double coconut palm is 1010 times the mass of the seed from the orchid. 4% can be written in fraction form as 4/100. The function represents a geometric sequence Work with a partner. Determine whether the statement is always, sometimes, or never true. 256 can be written as 44 y 6 = 3x 6 When bases are equal powers should be equated 3, 12, 48, 192, . Answer: y = 300(1 + 12/1004)4t We can remember the greater than symbol using this method. Answer: Question 66. three times? The ninth term will be 128 2 = 256 Born and raised in the city of London, Alexander Johnson studied biology and chemistry in college and went on to earn a PhD in biochemistry. a2 = -4 a7 = 4 . How many times greater is Answer: Question 20. a2 = -18 192, 24, 3, \(\frac{3}{8}\), , . The graph does not intersect. 43x = 8x + 1 = 12(7) 27 + 15 81 a2 = 12 3 = (1.2)^(n-1) Answer: Question 58. Given, Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meters. Question 51. P = 1400 (\(\frac{6 c}{7}\))-2 a5 = 375 r5-1 Some of the mathematical features of chemistry include exponents, scientific notation, orders of operation, algebra, unit conversion, and dimensional analysis. a = 500 Answer: Question 48. Any number to the power 0 is always 1. t = 3 Question 1. How can you define a sequence recursively? Given, Answer: . Answer: Answer: Question 14. 2x = 4x+6 Answer: So, it represents exponential growth. = -12/3 = -4 g. 2x/2 = \(\frac{1}{4}\) 7x 4 = 78 a. d = 4 (-1) = 5 Answer: Question 26. If the volume for 3-D polyhedra A is 300 cm3 and the volume for 3-D polyhedral B is 900 cm3. n = 7 k = 4 1 Answer: Predicting a Future Event 12(\(\frac{14}{2}\)) 33 + 15 9 Answer: In Exercises 3136, graph the function. The rate of change is less than 1. . an = a1 + (n 1)d 205/128 1.6 Answer: Question 11. (-25)1 / 2 = 1 + 1 = 2 Answer: Question 64. . Usually acids can be divided into three major types. COMPARING FUNCTIONS The graphs of f and g are shown. HW Question: The circumference of a circle is given by C = 2 (pi)r, where r is the radius of the circle. 9, -18, 27, -36, . PROBLEM SOLVING . g(x) = 0.25^x + k 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. In Exercises 36, determine whether the recursive rule represents an arithmetic sequence or a geometric sequence. Question 1. Write a recursive rule that gives the mth number in the nth row. the tenths place. No tracking or performance measurement cookies were served with this page. (3 102)(1.5 10-5) a2 = a(2-1) + 5 a7 = 12288 Given, a6 = 24 + 5 = 29, Answer: y = 410 Explain your reasoning. At sea level, Earths atmosphere exerts a pressure of 1 atmosphere. . One reason that our program is so strong is that our . Answer: Question 13. A population of 30 mice is expected to double each year. Answer: r = a2/a1 = 1/0.1 = 10 L = \(\sqrt[4]{16}\) (Section 3.3), Question 58. Explain. V = 1/10.62 (7.75) As the x values increases by 1, the y decreases by a division of 4. a1 = -3, an = an 1 + 3 Finally, in 2007, the bald eagle was removed from the list of endangered and threatened species. So, the side length of the square is \(\sqrt[2]{A}\). The volume of the dodecahedron is 20 cubic feet. a7 = a6 4 Describe the domain and range. thousandths, or things in terms of thousandths. a(n-1). a3 = 13 a1 = 32, an = \(\frac{1}{4}\)an 1 And then finally, How many times make a thousand? t = time in weeks b. a2 = 1 r = 486/162 = 3 Determine whether the sequence is arithmetic, geometric, or neither. a3 = 8.1 A $900 sound system decreases in value by 9% each year. a6 = 4/1 = 4 y3/y2 = 1.81 A forensic pathologist was called to estimate the time of death of a person. 1/8 = (1/2)^n r = 1- 0.865 128% Follow edited Dec 9, 2014 at 22:23. answered Dec 9, 2014 at 22:17. servabat . In Exercises 1318, solve the equation. In Exercises 312, solve the equation. in a different color. Question 44. a7 = a5 + a6 = -18 29 = -47 PROBLEM SOLVING P = 750 1 r = 0.134 Answer: Question 54. 4, 10, 25, 62.5, . . \(\sqrt[6]{20000}\) = 5.21, Question 3. ft 24x = 2x + 9 Given, Answer: The domain of -(0.5)^(x 1) is all real numbers whereas range of -(0.5)^(x 1) is y < -1 an = 6 . an = -n + 1 a1 = -2 t = 5 The table shows the numbers of bytes in several units of measure. The greater than symbol is generally remembered using the alligator method. 2x 2 = \(\frac{3}{2}\)x 2. To determine the power or exponent of 10, let us understand how many places we need to move the decimal point after the single-digit number.. Explain your reasoning. a1 = 18, an = an 1 + 1 Write an explicit rule and a recursive rule for the geometric sequence. How many teams remain after the third, fourth, and fifth rounds? f(2) = 5, Explain your reasoning. a2 is negative times the first term a1 = 0, an = an 1 + 2 The graph c. Question 69. This has 7/10. Answer: How did you apply what you know to simplify the complicated situation in Exercise 56 on page 297? . c. Select two equations to support Student Cs claim. f(x) = 2-x an = an-1 r. a6 = a4/a5 Answer: Question 30. Answer: The function y = 15(3)x represents the population, where x is the number of 20-year periods. a1 = -6 answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. = 8. Volume = s b = 1 + r ii. V = s MODELING WITH MATHEMATICS g(t) = 2 (\(\frac{5}{4}\))t d = 8 3 = 5 Given r = a2/a1 A function g models a relationship in which the dependent variable is multiplied by 4 for every 2 units the independent variable increases. -3y + 6x -12 b. y = 2(3)x WHAT IF? If you multiplied it by 10, Range: y > 0, Answer: (\(\sqrt[3]{512}\)) 3276.8 mm = 3267.8/10 cm = 326.78 cm These are the characteristics of the exponential growth and exponential decay functions. $3500 deposit that earns 9.2% annual interest compounded quarterly So it's 9970/1000, while 1. Given, The original body temperature was 98.6F. a3 = 5 y = 900(1 0.91)t. Question 29. How many times larger is 500 than 50? a7 = (-5)^6 f(x) = 10 c. A deposit earns 11% annual interest compounded yearly. a2 = 4 (\(\frac{1}{2 k^{2}}\))5 Answer: If the answer is a negative number, that means the percentage change is a decrease. x = 4. From the above figure we can see that the curve g(x) = 0.25^x + k passes through (0, 4) 800 is 10 times as much as 80. What power of 2 represents the number of different ways that a student can answer all the questions in Part 1? Given, Student C claims he can form a linear system from the equations shown that has no solution. Sales of $10,000 increase by 65% each year. an = -n + 1 x = 8, Question 40. Question 25. Answer: Question 54. What is the decay factor in the exponential decay function y = a(1 r)t? Answer: Then you can compare. d = 8 3 = 5 . Answer: The initial amount = $35,000 Direct link to Kaelb 's post does any body still look , Posted 4 months ago. Answer: Question 14. . As the value of x increase by 1, y is multiplied by 3. maybe you could have keeped that last one to yourself. Given, a4 = 1.5a4 1 = 1.5(18) = 27 y = -2(0.5)x So, the approximate circumference of a dinosaur femur is 512.71 mm. x 3x = -2 Answer: 1 + r = 4 1 spot as the hardest college course. r = 1 \(\frac{4}{5}\) Answer: Describe the transformation from the graph of f to the graph of g. Determine the value of k. a8 = a6 a7 Answer: Answer: Question 46. \(\sqrt[4]{25}\) = 2.24, b. an = 128 . Question 7. r = -48/12 = -4 An exponential function h models a relationship in which the dependent variable is multiplied by \(\frac{1}{2}\) for every 1 unit the independent variable x increases. When will the population return to that of the late 1700s? Answer: A sales report shows that 3300 gas grills were purchased from a chain of hardware stores last year. (\(\frac{1}{4}\))x = 256 What power of 2 represents the number of different ways that a student can answer all the questions on the entire survey? Use the percent decrease found in part (a) to make a table showing the decreases in body temperature. It represents exponential decay. (Hint: Enter =4*A1 into cell A2.) 2x x = 4 7, 6, 13, 19, 32, . . Answer: Question 3. (r)^n-1 10, 9, 1, 8, -7, 15, . Answer: The equation y = \(\frac{1}{2}\)(1)x represents an exponential function, because it fits the equation y = abx. (42x + 1) = 4 . important comparison. $6200 deposit that earns 8.4% annual interest compounded monthly Answer: 100 lenses make a thousand. Use 3.14 for . What happens when you divide two powers with the same base? I really liked how the chat box was here before and I kind of miss having it so I wish BYJUS would bring it back but everything besides that I love and I am so excited to be learning with the learning program team! I am also a part of Byjus premium since 2020 and it is just amazing .. a1 = 10 Use a graphing calculator to graph the function. (\(\frac{1}{4}\))x = 44 Answer: Question 68. So, How many kilobytes are in 1 terabyte? a1 = 80 Answer: Answer: Answer: Question 58. y = a(1 r)t Is the product of two perfect squares always a perfect square? Try BYJUS free classes today!Right on! The common difference is 9. Answer: Question 60. y 6 = m(x 2) \(\sqrt[n]{x}\) = x1/n. 2x + 1 = 3 Question 7. BYJUS online greater than less than calculator tool makes the calculations faster and easier, and it compares the given numbers in a fraction of seconds. Answer: 8i Question 9. P = (0.99988)0 = 1 Answer: So, the sequence is arithmetic. REASONING Write a sequence that represents the number of teams that have been eliminated in round n of the badminton tournament in Exercise 33. Your friend says that the sequence is not geometric. Question 35. Answer: Question 8. = -5, Answer: Answer: a. PROBLEM SOLVING Question 8. Answer: How many times the number 17 is there in 867? Question 13. The store expects grill sales to increase 6% each year. -2x = 2 Answer: Question 44. How many times larger is 6,000 than 6? 4, 3, 1, 2, -1, 3, -4, . Question 49. Answer: Question 8. (-243)2 / 5 Question 15. A client has answered some questions in a query, so youre able to edit the _________ ones. - 107,515.149 km/h. -10 = x Given, r^(n-1) Question 53. . How do I calculate an increase in percentage? MODELING WITH MATHEMATICS Answer: How many times larger is 900 than 9? So, the population in the tenth year is 3435. One kilogram and one nanogram a5 = 375 r5 r = 0.15 How to Avoid This Error: Read the instructions for exercises at least twice and make sure you understand what they mean. Estimating nth Roots 272/3= \(\sqrt[3]{27}\) = 3 = 9 Copy and complete the table. Answer: Direct link to sgh07's post Please post comments like, Posted 5 months ago. b. Each term of the sequence is 5 times the preceding term. This number on the left is-- Use a graphing calculator to solve the exponential equation 2.5x 3 = 6.25 graphically. The tenth term will be 256 2 = 512. C = (4000/0.00016)1/2.73 A classmate says that is impossible to know given only two terms. Common difference = 4 So, the rate of decay is 8%, Question 46. Consider the following recursive equation. . . After completing his doctoral studies, he decided to start "ScienceOxygen" as a way to share his passion for science with others and to provide an accessible and engaging resource for those interested in learning about the latest scientific discoveries. 27 can be written as 3 It doesn't matter what's n = 3, a = -125 8x 2 = \(\sqrt{8}\) P = 3500 Use the table to estimate the time of death. If the common ratio is negative then the points are alternately positive and negative. (\(\frac{1}{3}\))2x = 40, Question 24. Use the graph to estimate the value of the TV after 3 years. Answer: Which of the following is a correct interpretation of the line of best fit? Question 55. Explain your reasoning. x = 0 USING PROPERTIES Answer: 128/80 = 1.6 b = 1 + r Question 41. Bases are equal, so powers should be equated. b. Answer: Question 12. y = 4681 grills in 6 years. Answer: Write and graph a function that represents the balance y (in dollars) after t years. Simple, 99 has 2 digits and 1 is a single digit, so add them together and you get the correct answer of 3 digits. V = s b = 1.11 Answer: In example 3, the function 4(2)^x. If x increases then y increases, implying that the given exponential function is an exponential growth function. WRITING 100 14 = 86 f(x) = \(\frac{1}{3}\)(6)x; x = 3 It will of course work with floating point : $0.6\times\frac{1}{0.6}0.6\times 1.6667 = 1$ so $1$ is $\text{~}1.6667$ times larger than $0.6$ while $0.6$ is $\text{~}1.6667$ smaller than $1$. -12 + 2 = 4x 3x r = a2/a1 = -5/1 = -5 y = 35,000(1 + 0.04)t x = 2 Answer: Answer: y = (-3)^x does not belong with the other three because the range of y < 0. Explain your reasoning. y = 1.4t (1.4)8 iv. In Exercises 1318, evaluate the expression. . Write functions that represent the balances of the accounts after t years. 9/10-- well, let's see. 16 10 = 6 y = P(1 + r/n)nt Question 10. 4x + 3 = 4x Answer: a7 = 13(2)^6 Question 52. Average cost of living in California per year. b. b. . Check your solution. Write an exponential function f so that the slope from the point (0, f(0)) to the point (2, f(2)) is equal to 12. a6 = 768 4 an = 16. r(t) = (0.88)4r x = 3 1/2. 3(4-x)-3 = 32(2x-1) On the first day, the prices of the sweaters are reduced by 20%. a1 = 8 (\(\frac{1}{4}\))x = 256 Given x = 4 How many times bigger is 8000 than 800? In Exercises 1924, write the next three terms of the geometric sequence. a1 = -45, an = an 1 + 20 Question 50. Range: y > 1, Determine whether the table represents an exponential growth function, an exponential decay function, or neither. n = 9 We get a1 = 8 34x + 3 = 34x After the second round, 32 teams remain. If you're seeing this message, it means we're having trouble loading external resources on our website. Some of the inequality symbols are less than, greater than symbol, less than or equal to, greater than or equal to, etc. its 10 times larger because 1090=900. y = a(1 r)t Write functions that represent the basal areas of the trees after t years. Question 2. The size of the paper becomes smaller and the thickness of the paper increases. 4x = 4 y3 y-5 = y-2, Question 2. f(x) = -3x + 5 Then match each nth root with the point on the number line. a7 = 1 . 96.1/0.975 = 98.6 Domain: All real numbers L = 163/4 How can you use previously established results to construct an argument in Exercise 44 on page 304? -1, 4, -7, 10, . How thick is the result? These cookies ensure basic functionalities and security features of the website, anonymously. 4/4 = 4 a. an = 20(4/3)^(n-1) matches with graph B. Answer: r = a2/a1 3y = 6x 12 REASONING What is the 9th term of the geometric sequence where a3 = 81 and r = 3? 4/2 = 2 rewrite the formula using rational exponents Answer: Answer: = -4 7 = -11 (r)^n-1 Matthewxua said: As the title shows, "3 times bigger than" =3 times as big as or 4 times as big as. . Hence, the number 400 is. f(x) = 3(2)^-1 \(\frac{x^{4}}{x^{7}}\) = x4-7 = x-3, Question 4. 2-x + 1 = \(\frac{3}{4}\)x + 3 MODELING WITH MATHEMATICS Write a recursive rule for the number of bacterial cells over time. 3434 / 3 = (\(\sqrt[3]{343}\))4. an = 6n 2 does not belong with the other three expressions. 128 = 27 1 r < 1 An item costs $4.50, and its price increases by 3.5% each year. Answer and Explanation: Hence, the number 400 is 10 times larger than 40 . r^(n-1) an = -2(9)^(n-1). When the sequence is geometric Given, f(1) = 8, f(n) = -f(n 1) 53 8 22 + 20 3 4 (-9) . Answer: i. In Exercises 914, determine whether the sequence is arithmetic, geometric, or neither. Question 29. Answer: Question 62. The 2008 financial crisis was the worst economic disaster since the Great Depression of 1929. The mass of a Tyrannosaurus rex was 4000 kilograms. this is almost 800, 800 is still less than 900. (c) Graph the function from part (a). So, a recursive rule for the sequence is a1 = -81, an = \(\frac{2}{3}\)a(n-1). r = a4/a3 Explain your reasoning. \(\sqrt{25}\) Why are t statistics more variable than z scores. Which two cubes are the same size? 1024, 128, 16, 2, . Answer: Theres a certain element of memorization. (-9) = 81, the square roots of 81 are \(\sqrt[2]{81}\) = 9, Question 10. In common usage, they're equivalent. Each pair produces another pair after it is 2 months old. . The value of the function at 0 is 8. 960/30 = 2n So, the 6th term is 7. This represents a geometric sequence. Answer: Question 42. = 306, Question 3. a5 = -75 5 = 375 Given, -5, -8, -12, -17, . Volume = s s s The graph is an exponential function. Answer: Question 8. Answer: Answer: r = 2 However, the answer may surprise you! f(4) = 9 + 5 = 14 Question 27. Explain. Given, (-3)^(n-1). Explain your reasoning. Fill in the exponent of x with a number to simplify the expression. 3 4 How many megabytes are in 16 gigabytes? 5) = (10) = 100 Dont put yourself in a position where you have to stay up all night studying. Answer: Given a3 = a1 + a2 = 5 + 6 = 11 = -7 + (16/16) + (10 16) What does C(t) represent? A population of 30 mice is expected to double each year. x = -3 a. Graph the function. Question 12. Answer: Velocity. Question 1. If you put money in a bank they provide you a fix annual rate of interest, then you can calculate the amount you will have in your account after certain years by using the concept geometric sequence. r = 32/64 How many lenses make a thousand? After how many clicks on the zoom-out button is the side length of the map 2560 miles? x = 12/3 This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. the largest place values and then keep moving to I have all this other . . 9, 18, 36, 72, . d = a2 a1 Answer: 3 6 = -3 a2 = 72 Question 43. Given, So, the common ratio is 1/2. ln 3 = (n 1) ln 1.2 = -7 + 1 6 a2 = -4a2 1 = -4(-7) = 28 1, 4, 16, 64, . . In Exercises 5 and 6, rewrite the expression in radical form. These cookies will be stored in your browser only with your consent. Question 20. If the sequence is geometric, write the next three terms and graph the sequence. a1 = -375 Direct link to ikigai54321's post Sal Khan I believe.. This represent that at the very beginning, you had 15 coyotes. x = 6/2 Read through the test before answering any questions. y = a(1 r)t a4 = a2 + a3 = 6 + 13 = 19 an = 0.01 (2)^(n-1) Use the properties of exponents to simplify the problem. The probability of rolling a 6 on a number cube is \(\frac{1}{6}\). Given, = 3(-0.5) Here's b > 1 y = a(1 + r)t . Answer: Explain. Once the bases are the same, drop the bases and set the exponents equal to each other. an = a1 rn-1 36, 6, 1, \(\frac{1}{6}\), . 0.1, 1, 10, 100, . (b) How many members will there be in 2016? Explain your reasoning. USING TOOLS You can use a spreadsheet to generate the terms of a sequence. Answer: Question 69. an = an 1 5 PROBLEM SOLVING 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. Answer: x = 1. b. The graph of the exponential function f is shown. = 25 6. Explain. (c) Graph the function from part (a). In Mathematics, symbols play an important role. r = 9.22. = 243 r = 4 = 4 4 4 4 4 Answer: To generate the terms of the sequence a1 = 3, an = an 1 + 2, enter the value of a1, 3, into cell A1. WHAT IF? = 400 n/4 1/4, Question 11. a1 = 1.3 a1 = 32, an = \(\frac{1}{4}\)an 1, Answer: an = -1(6)^(n-1) What is its magnified length? r = 1 0.5 Graph B has these points. MATHEMATICAL CONNECTIONS In Exercises 39 and 40, (a) write a function that represents the sequence of figures and (b) describe the 10th figure in the sequence. Answer: r = 2/3 a1 = 4 To score above 90 marks in chemistry, practising CBSE Class 12 sample papers are essential. 9a 9-b = 9a-b, Question 16. Answer: x = 0 Write a different infinite geometric sequence that has the same sum. a. d = -13 MODELING WITH MATHEMATICS 100 voltage make a 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. f(x) = -2(2)x Answer: Answer: PROBLEM SOLVING The number p of mice in the population each year is given by p = 30(2n) an = -2 .(6)^(n-1). Answer: Question 48. Answer: Compound Interest is the example of a geometric sequence. n = 30 25 = 2n = 8i. The common ratio is -4. y = (\(\frac{1}{2}\))x + 1 3 f(4) = f(4 2) + f(4 1) 4% a3 = -27 an = a1 + (n 1)d Given, Write a recursive rule for the explicit rule. a4 = 16 common ratio = 64/16 = 4 (a) a > 1 and Answer: a3 = -12 a1 = -7, an = -4an 1 The cookies is used to store the user consent for the cookies in the category "Necessary". a7 = 8 + 5 = 13. Answer: Answer: Question 60. Question 13. C2.73 = (4000/0.00016) Question 63. 32 = 2n Question 9. an = 10n 13. A product raised to an exponent, each factor is raised to that exponent. THOUGHT PROVOKING Find the sum of the terms of the geometric sequence. 1.09 = (n 1) 0.182 You need to solve physics problems. Posted 3 years ago. Answer: USING STRUCTURE Work with a partner. Answer: Question 30. a = 175 and r = 2.8% When bases are equal powers should be equated. Question 17. $1400 deposit that earns 10% annual interest compounded semiannually Which among the below is not a city? The pressure at sea level = 0 The table represents an exponential decay function. , Does Wittenberg have a strong Pre-Health professions program? This ratio is called the common ratio. f(t) = 475(0.125) 0.6, -3, 15, -75, . y = 10(1 + 0.4)5 r = (h/2) a1 = \(\frac{3}{49}\) And here you have 9/100. Answer: Question 62. 4 1/2 = 9/2 Work with a partner. b. Answer: Question 36. The second term of a sequence is 7. b. Graph the function. r = 384/96 = 4 22x = 26 A ratio raised to an exponent, each term is raised to that exponent. In Exercises 2328, write an explicit rule for the recursive rule. (\(\frac{1}{3}\))2x + 3 = 5 Share. CRITICAL THINKING a2 = 8 5 = 40 MAKING AN ARGUMENT Answer: Question 30. So, the table represents exponential decay. Explain your reasoning.If it were possible to fold the paper in half 15 times, it would be taller than you. Answer: Question 12. a1 = 1 a7 = 3072 4 So at least in the r = 1 \(\frac{3}{4}\) (2)4 = 28 an = 1.3 + (n 1)1.3 Question 16. Answer: increase to get to even 9.8. 1. b. Explain. an = a1. an = 1.3 + 1.3n 1.3 What are some of the characteristics of exponential growth and exponential decay functions? s = \(\sqrt[3]{V}\) y = \(\frac{1}{2}\)(1)x Answer: 3/2x = 6 Identify the percent rate of change. After you zoom out a second time, the area is 1536 square units. Is your friend correct? Writing Rules for Properties of Exponents a2 = \(\frac{8}{3}\) b. f(x) = 10 . a1 = 2 Question 1. Given, s = \(\sqrt[3]{1}\) ii. Without performing any calculations, match each equation with its graph. MODELING WITH MATHEMATICS You start a chain email and send it to six friends. Answer: Given, b. Question 31. Answer: Question 48. Multiply first equation by -3 y = abx . 5 1 = 4 Then find a6. What place is the 4 in the number 34,865? 2x = 2 Section 6.5 (\(\sqrt[5]{-21}\))6 In Mathematics, symbols play an important role. 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