8. 2 3x 1 = 16 is an example of a(n). SOLUTION: An equation in which the variable occurs as exponent is an exponential equation.

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1 Choose the word or term that best completes each sentence. 1. 7xy 4 is an example of a(n). A product of a number and variables is a monomial. 2. The of 95,234 is ,234 is almost 100,000 or 10 5, so 10 5 is its order of magnitude is a(n) of 8. Since 8 = 2 3, 2 is the cube root of The rules for operations with exponents can be extended to apply to expressions with a(n) such as. The exponent is a rational exponent. 5. A number written in is of the form a 10 n, where 1 a < 10 and n is an integer. A number written as a 10 n, where 1 a < 10 and n is an integer, is written in scientific notation. 6. f (x) = 3 x is an example of a(n). A function in the form y = ab x, where a 0, b > 0, and b 1 is an exponential function. 7. is a(n) for the sequence. A formula that gives the first term of a sequence and tells you how to find the next term when you know the preceding term is called a recursive formula x 1 = 16 is an example of a(n). An equation in which the variable occurs as exponent is an exponential equation. 9. The equation for is y = C(1 r) t. Since 0 < 1 r < 1, this is an example of exponential decay. esolutions Manual - Powered by Cognero Page 1

2 10. If a n = b for a positive integer n, then a is a(n) of b. If a n = b for a positive integer n, then a is an nth root of b. Simplify each expression. 11. x x 3 x (2xy)( 3x 2 y 5 ) 13. ( 4ab 4 )( 5a 5 b 2 ) 14. (6x 3 y 2 ) 2 esolutions Manual - Powered by Cognero Page 2

3 15. [(2r 3 t) 3 ] ( 2u 3 )(5u) 17. (2x 2 ) 3 (x 3 ) (2x 3 ) 3 esolutions Manual - Powered by Cognero Page 3

4 19. GEOMETRY Use the formula V = πr 2 h to find the volume of the cylinder. 20. Simplify each expression. Assume that no denominator equals zero. 21. esolutions Manual - Powered by Cognero Page 4

5 a 3 b 0 c esolutions Manual - Powered by Cognero Page 5

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7 GEOMETRY The area of a rectangle is 25x 2 y 4 square feet. The width of the rectangle is 5xy feet. What is the length of the rectangle? The length of the rectangle is 5xy 3 ft. Simplify. 29. esolutions Manual - Powered by Cognero Page 7

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9 Solve each equation x = 7776 Therefore, the solution is x 1 = 32 Therefore, the solution is. esolutions Manual - Powered by Cognero Page 9

10 Express each number in scientific notation ,300,000 2,300, The decimal point moved 6 places to the left, so n = 6. 2,300,000 = The decimal point moved 5 places to the right, so n = = ASTRONOMY Earth has a diameter of about 8000 miles. Jupiter has a diameter of about 88,000 miles. Write in scientific notation the ratio of Earth s diameter to Jupiter s diameter. Earth: 8000 = Jupiter: 88,000 = In scientific notation, the ratio of Earth s diameter to Jupiter s diameter is about esolutions Manual - Powered by Cognero Page 10

11 Graph each function. Find the y-intercept, and state the domain and range. 42. y = 2 x Complete a table of values for 2 < x < 2. Connect the points on the graph with a smooth curve. x 2 x y The graph crosses the y-axis at 1. The domain is all real numbers, and the range is all real numbers greater than 0. esolutions Manual - Powered by Cognero Page 11

12 43. y = 3 x + 1 Complete a table of values for 2 < x < 2. Connect the points on the graph with a smooth curve. x 3 x + 1 y The graph crosses the y-axis at 2. The domain is all real numbers, and the range is all real numbers greater than 1. esolutions Manual - Powered by Cognero Page 12

13 44. y = 4 x + 2 Complete a table of values for 2 < x < 2. Connect the points on the graph with a smooth curve. x 4 x + 2 y The graph crosses the y-axis at 3. The domain is all real numbers, and the range is all real numbers greater than 2. esolutions Manual - Powered by Cognero Page 13

14 45. y = 2 x 3 Complete a table of values for 2 < x < 2. Connect the points on the graph with a smooth curve. x 2 x 3 y The graph crosses the y-axis at 2. The domain is all real numbers, and the range is all real numbers greater than BIOLOGY The population of bacteria in a petri dish increases according to the model p = 550(2.7) 0.008t, where t is the number of hours and t = 0 corresponds to 1:00 P.M. Use this model to estimate the number of bacteria in the dish at 5:00 P.M. If t = 0 corresponds to 1:00 P.M, then t = 4 represents 5:00 P.M. There will be about 568 bacteria in the dish at 5:00 P.M. esolutions Manual - Powered by Cognero Page 14

15 47. Find the final value of $2500 invested at an interest rate of 2% compounded monthly for 10 years. Use the equation for compound interest, with P = 2500, r = 0.02, n = 12, and t = 10. The final value of the investment is about $ COMPUTERS Zita s computer is depreciating at a rate of 3% per year. She bought the computer for $1200. a. Write an equation to represent this situation. b. What will the computer s value be after 5 years? a. Use the equation for exponential decay, with a = 1200 and r = The equation that represents the depreciation of Zita s computer is y = 1200(1 0.03) t. b. Substitute 5 for t and solve. After 5 years, Zita s computer value is about $ Find the next three terms in each geometric sequence , 1, 1, 1,... Calculate the common ratio. The common ratio is 1. Multiply each term by the common ratio to find the next three terms. 1 1 = = = 1 The next three terms of the sequence are 1, 1, and 1. esolutions Manual - Powered by Cognero Page 15

16 50. 3, 9, Calculate the common ratio. The common ratio is 3. Multiply each term by the common ratio to find the next three terms = = = 729 The next three terms of the sequence are 81, 243, and , 128, 64,... Calculate the common ratio. The common ratio is. Multiply each term by the common ratio to find the next three terms. 64 = = = 8 The next three terms of the sequence are 32, 16, and 8. Write the equation for the nth term of each geometric sequence , 1, 1, 1,... The first term of the sequence is 1. So, a 1 = 1. Calculate the common ratio. The common ratio is 1. So, r = 1. esolutions Manual - Powered by Cognero Page 16

17 53. 3, 9, 27,... The first term of the sequence is 3. So, a 1 = 3. Calculate the common ratio. The common ratio is 3. So, r = , 128, 64,... The first term of the sequence is 256. So, a 1 = 256. Calculate the common ratio. The common ratio is. So, r =. 55. SPORTS A basketball is dropped from a height of 20 feet. It bounces to its height each bounce. Draw a graph to represent the situation. Compared to the previous bounce, the ball returns to its height. So, the common ratio is. Use common ratio to find next y term esolutions Manual - Powered by Cognero Page 17

18 Therefore, the geometric sequence that models this situation is 20, 10, 5,,,,,, and so forth. esolutions Manual - Powered by Cognero Page 18

19 Find the first five terms of each sequence. 56. Use a 1 = 11 and the recursive formula to find the next four terms. The first five terms are 11, 7, 3, 1, and 5. esolutions Manual - Powered by Cognero Page 19

20 57. Use a 1 = 3 and the recursive formula to find the next four terms. The first five terms are 3, 12, 30, 66, and 138. Write a recursive formula for each sequence , 7, 12, 17,... Subtract each term from the term that follows it. 7 2 = 5; 12 7 = 5, = 5 There is a common difference of 5. The sequence is arithmetic. Use the formula for an arithmetic sequence. The first term a 1 is 2, and n 2. A recursive formula for the sequence 2, 7, 12, 17, is a 1 = 2, a n = a n 1 + 5, n 2. esolutions Manual - Powered by Cognero Page 20

21 59. 32, 16, 8, 4,... Subtract each term from the term that follows it = 16; 8 16 = 8, 4 8 = 4 There is no common difference. Check for a common ratio by dividing each term by the term that precedes it. There is a common ratio of 0.5. The sequence is geometric. Use the formula for a geometric sequence. The first term a 1 is 32, and n 2. A recursive formula for the sequence 32, 16, 8, 4, is a 1 = 32, a n = 0.5a n 1, n , 5, 11, 23,... Subtract each term from the term that follows it. 5 2 = 3; 11 5 = 6, = 12 There is no common difference. Check for a common ratio by dividing each term by the term that precedes it. There is no common ratio. Therefore the sequence must be a combination of both. From the difference above, you can see each is twice as big as the previous. So r is 2. From the ratios, if each denominator was one less, the ratios would be 0.5. Thus, the common difference is 1. Then, if the first term a 1 is 2, and n 2, a recursive formula for the sequence 2, 5, 11, 23, is a 1 = 2, a n = 2a n 1 + 1, n 2. esolutions Manual - Powered by Cognero Page 21

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