Question 1 of 40 2 5 Points Use properties of logarithms to expand the following logarithmic expression as much as possible log b (x 2 y) z 2 A 2 log b x log b y 2 log b z B 4 log b x log b y 2 log b z C 2 log b x 2 log b y 2 log b z D log b x log b y 2 log b z Question 2 of 40 2 5 Points Write the following equation in its equivalent logarithmic form 38 2 A Log 2 3 1 8 B Log 8 2 1 3 C Log 2 8 1 2 D Log 3 2 1 8 Question 3 of 40 2 5 Points Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents e x 1 1 e A 3 B 2 C 4 D 12 Question 4 of 40 2 5 Points Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents 3 1 x 1 27 A 2 B 7 C 4 D 3 Question 5 of 40 2 5 Points The half life of the radioactive element krypton 91 is 10 seconds If 16 grams of krypton 91 are initially present, how many grams are present after 10 seconds 20 seconds A 10 grams after 10 seconds 6 grams after 20 seconds B 12 grams after 10 seconds 7 grams after 20 seconds C 4 grams after 10 seconds 1 gram after 20 seconds D 8 grams after 10 seconds 4 grams after 20 seconds Question 6 of 40 2 5 Points Consider the model for exponential growth or decay given by A A 0 e kt If k , the function models the amount, or size, of a growing entity If k , the function models the amount, or size, of a decaying entity A 0 0 B 0 0 C 0 0 D 0 0 Question 7 of 40 2 5 Points The exponential function f with base b is defined by f(x) , b 0 and b 1 Using interval notation, the domain of this function is and the range is A bx (, ) (1, ) B bx ( , ) (2, ) C bx ( , ) (0, ) D bx ( , ) ( 1, ) Question 8 of 40 2 5 Points The graph of the exponential function f with base b approaches, but does not touch, the axis This axis, whose equation is , is a asymptote A x y 0 horizontal B x y 1 vertical C x y 0 horizontal D x y 1 vertical Question 9 of 40 2 5 Points Approximate the following using a calculator round your answer to three decimal places 3 5 A 765 B 14297 C 11 494 D 11 665 Question 10 of 40 2 5 Points You have $10,000 to invest One bank pays 5 interest compounded quarterly and a second bank pays 4 5 interest compounded monthly Use the formula for compound interest to write a function for the balance in each bank at any time t A A 20,000(1 (0 06 4)) 4t A 10,000(1 (0 044 14)) 12t B A 15,000(1 (0 07 4)) 4t A 10,000(1 (0 025 12)) 12t C A 10,000(1 (0 05 4)) 4t A 10,000(1 (0 045 12)) 12t D A 25,000(1 (0 05 4)) 4t A 10,000(1 (0 032 14)) 12t Question 11 of 40 2 5 Points Use properties of logarithms to condense the following logarithmic expression Write the expression as a single logarithm whose coefficient is 1 log x 3 log y A log (xy) B log (xy 3 ) C log (xy 2 ) D log y (xy) 3 Question 12 of 40 2 5 Points Write the following equation in its equivalent exponential form 5 log b 32 A b 5 32 B y 5 32 C B log5 32 D Log b 32 Question 13 of 40 2 5 Points Use the exponential growth model, A A 0 e kt , to show that the time it takes a population to double (to grow from A 0 to 2A 0 ) is given by t ln 2 k A A 0 A 0 e kt ln e kt ln 2 ln e kt ln 2 kt ln 2 k t B 2A 0 A 0 e 2 e kt ln ln e kt ln 2 kt ln 2 k t C 2A 0 A 0 e kt 2 e kt ln 2 ln e kt ln 2 kt ln 2 k t D 2A 0 A 0 e kt 2 e kt ln 1 ln e kt ln 2 kt ln 2 k t oe Question 14 of 40 2 5 Points An artifact originally had 16 grams of carbon 14 present The decay model A 16e 0 000121t describes the amount of carbon 14 present after t years How many grams of carbon 14 will be present in 5715 years A Approximately 7 grams B Approximately 8 grams C Approximately 23 grams D Approximately 4 grams Question 15 of 40 2 5 Points Solve the following exponential equation Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution e x 5 7 A ln 5 7 1 74 B ln 8 7 3 74 C ln 6 9 2 49 D ln 8 9 3 97 Question 16 of 40 2 5 Points Evaluate the following expression without using a calculator 8 log8 19 A 17 B 38 C 24 D 19 Question 17 of 40 2 5 Points Use properties of logarithms to expand the following logarithmic expression as much as possible Log b (xy 3 z 3 ) A 1 2 log b x 6 log b y 3 log b z B 1 2 log b x 9 log b y 3 log b z C 1 2 log b x 3 log b y 6 log b z D 1 2 log b x 3 log b y 3 log b z Question 18 of 40 2 5 Points Evaluate the following expression without using a calculator Log 7 7 A 1 4 B 3 5 C 1 2 D 2 7 Question 19 of 40 2 5 Points Write the following equation in its equivalent logarithmic form 2 4 1 16 A Log 4 1 16 64 B Log 2 1 24 4 C Log 2 1 16 4 D Log 4 1 16 54 Question 20 of 40 2 5 Points Use properties of logarithms to condense the following logarithmic expression Write the expression as a single logarithm whose coefficient is 1 3 ln x 1 3 ln y A ln (x y 1 2 ) B ln x (x 6 y 1 3 ) C ln (x 3 y 1 3 ) D ln (x 3 y 1 4 ) Question 21 of 40 2 5 Points Perform the long division and write the partial fraction decomposition of the remainder term x 4 x 2 2 x 3 x 2 A x 3 2 x 1 x 2 4x 1 B 2x 1 2 x 2 x 2 x 1 C 2x 1 2 x 2 2 x 5 x 1 D x 1 2 x 2 x 2 2 x 1 Question 22 of 40 2 5 Points Solve each equation by the substitution method x y 1 x 2 xy y 2 5 A (4, 3), ( 1, 2) B (2, 3), ( 1, 6) C ( 4, 3), ( 1, 3) D (2, 3), ( 1, 2) Question 23 of 40 2 5 Points Write the partial fraction decomposition for the following rational expression x 4 x 2 (x 4) A 1 3x 1 x 2 x 5 4(x 2 4) B 1 5x 1 x 2 x 4 4(x 2 6) C 1 4x 1 x 2 x 4 4(x 2 4) D 1 3x 1 x 2 x 3 4(x 2 5) Question 24 of 40 2 5 Points Solve each equation by either substitution or addition method x 2 4y 2 20 x 2y 6 A (5, 2), ( 4, 1) B (4, 2), (3, 1) C (2, 2), (4, 1) D (6, 2), (7, 1) Question 25 of 40 2 5 Points Write the form of the partial fraction decomposition of the rational expression 7x 4 x 2 x 12 A 24 7(x 2) 26 7(x 5) B 14 7(x 3) 20 7(x 2 3) C 24 7(x 4) 25 7(x 3) D 22 8(x 2) 25 6(x 4) Question 26 of 40 2 5 Points Find the quadratic function y ax 2 bx c whose graph passes through the given points ( 1, 4), (1, 2), (2, 5) A y 2x 2 x 6 B y 2x 2 2x 4 C y 2x 2 2x 3 D y 2x 2 x 5 Question 27 of 40 2 5 Points Write the partial fraction decomposition for the following rational expression ax b (x c) 2 (c 0) A a a c ac b (x c) 2 B a b c ac b (x c) C a a b ac c (x c) 2 D a a b ac b (x c) Question 28 of 40 2 5 Points Solve the following system 2x 4y 3z 2 x 2y z 0 4x y z 6 A ( 3, 2, 6) B (4, 8, 3) C (3, 1, 5) D (1, 4, 1) Question 29 of 40 2 5 Points Write the partial fraction decomposition for the following rational expression 6x 11 (x 1) 2 A 6 x 1 5 (x 1) 2 B 5 x 1 4 (x 1) 2 C 2 x 1 7 (x 1) D 4 x 1 3 (x 1) Question 30 of 40 2 5 Points Solve the following system x y 4 3x 7y 18 A (2, 1) B (1, 4) C (2, 5) D (1, 3) Question 31 of 40 2 5 Points Solve the following system by the addition method 2x 3y 6 2x 3y 6 A (4, 1) B (5, 0) C (2, 1) D (3, 0) Question 32 of 40 2 5 Points Solve the following system 2x y 2 x y z 4 3x 2y z 0 A (2, 1, 4) B (1, 0, 3) C (0, 0, 2) D (3, 2, 1) Question 33 of 40 2 5 Points Let x represent one number and let y represent the other number Use the given conditions to write a system of equations Solve the system and find the numbers The sum of two numbers is 7 If one number is subtracted from the other, their difference is 1 Find the numbers A x y 7 x y 1 3 and 4 B x y 7 x y 1 5 and 6 C x y 7 x y 1 3 and 6 D x y 7 x y 1 2 and 3 Question 34 of 40 2 5 Points Write the partial fraction decomposition for the following rational expression 1 x 2 c 2 (c 0) A 1 4c x c 1 2c x c B 1 2c x c 1 2c x c C 1 3c x c 1 2c x c D 1 2c x c 1 3c x c Question 35 of 40 2 5 Points Write the form of the partial fraction decomposition of the rational expression 5x 2 6x 7 (x 1)(x 2 1) A A x 2 Bx 2 C x 2 3 B A x 4 Bx C x 2 1 C A x 3 Bx C x 2 1 D A x 1 Bx C x 2 1 Question 36 of 40 2 5 Points Many elevators have a capacity of 2000 pounds If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when x children and y adults will cause the elevator to be overloaded A 50x 150y 2000 B 100x 150y 1000 C 70x 250y 2000 D 55x 150y 3000 Question 37 of 40 2 5 Points Solve the following system by the substitution method x y 4 y 3x A (1, 4) B (3, 3) C (1, 3) D (6, 1) Question 38 of 40 2 5 Points Perform the long division and write the partial fraction decomposition of the remainder term x 5 2 x 2 1 A x 2 x 1 2(x 1) 4 2(x 1) B x 3 x 1 2(x 1) 3 2(x 1) C x 3 x 1 6(x 2) 3 2(x 1) D x 2 x 1 2(x 1) 4 2(x 1) Question 39 of 40 2 5 Points Solve the following system 3(2x y) 5z 1 2(x 3y 4z) 9 4(1 x) 3(z 3y) A (1, 1 3, 0) B (1 4, 1 3, 2) C (1 3, 1 5, 1) D (1 2, 1 3, 1) Question 40 of 40 2 5 Points Write the partial fraction decomposition for the following rational expression x 2 6x 3 (x 2) 3 A 1 x 4 2 (x 2) 2 6 (x 2) B 1 x 2 4 (x 2) 2 5 (x 1) 3 C 1 x 3 2 (x 3) 2 5 (x 2) D 1 x 2 2 (x 2) 2 5 (x 2) 3

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Question 1 of 40 2.5 Points Use properties of logarithms to expand the following logarithmic expression as much as possible. log b (x 2 y)

Question 1 of 40

2.5 Points

Use properties of logarithms to expand the following logarithmic expression as much as possible. log_b (x² y) / z²

A. 2 log_b x + log_b y - 2 log_b z
B. 4 log_b x - log_b y - 2 log_b z
C. 2 log_b x + 2 log_b y + 2 log_b z
D. log_b x - log_b y + 2 log_b z
Question 2 of 40	2.5 Points

Write the following equation in its equivalent logarithmic form. 38 = 2

A. Log₂ 3 = 1/8
B. Log₈ 2 = 1/3
C. Log₂ 8 = 1/2
D. Log₃ 2 = 1/8
Question 3 of 40	2.5 Points

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. e^x+1 = 1/e

A. {-3}
B. {-2}
C. {4}
D. {12}
Question 4 of 40	2.5 Points

Solve the following exponential equation by expressing each side as a power of the same base and then equating exponents. 3^1-x = 1/27

A. {2}
B. {-7}
C. {4}
D. {3}
Question 5 of 40	2.5 Points

The half-life of the radioactive element krypton-91 is 10 seconds. If 16 grams of krypton-91 are initially present, how many grams are present after 10 seconds? 20 seconds?

A. 10 grams after 10 seconds; 6 grams after 20 seconds
B. 12 grams after 10 seconds; 7 grams after 20 seconds
C. 4 grams after 10 seconds; 1 gram after 20 seconds
D. 8 grams after 10 seconds; 4 grams after 20 seconds
Question 6 of 40	2.5 Points

Consider the model for exponential growth or decay given by A = A₀e^kt. If k __________, the function models the amount, or size, of a growing entity. If k __________, the function models the amount, or size, of a decaying entity.

A. > 0; < 0
B. = 0; 0
C. 0; < 0
D. < 0; 0
Question 7 of 40	2.5 Points

The exponential function f with base b is defined by f(x) = __________, b > 0 and b 1. Using interval notation, the domain of this function is __________ and the range is __________.

A. bx; (, -); (1, )
B. bx; (-, -); (2, )
C. bx; (-, ); (0, )
D. bx; (-, -); (-1, )
Question 8 of 40	2.5 Points

The graph of the exponential function f with base b approaches, but does not touch, the __________-axis. This axis, whose equation is __________, is a __________ asymptote.

A. x; y = 0; horizontal
B. x; y = 1; vertical
C. -x; y = 0; horizontal
D. x; y = -1; vertical
Question 9 of 40	2.5 Points

Approximate the following using a calculator; round your answer to three decimal places. 3⁵

A. .765
B. 14297
C. 11.494
D. 11.665
Question 10 of 40	2.5 Points

You have $10,000 to invest. One bank pays 5% interest compounded quarterly and a second bank pays 4.5% interest compounded monthly. Use the formula for compound interest to write a function for the balance in each bank at any time t.

A. A = 20,000(1 + (0.06/4))^4t; A = 10,000(1 + (0.044/14))^12t
B. A = 15,000(1 + (0.07/4))^4t; A = 10,000(1 + (0.025/12))^12t
C. A = 10,000(1 + (0.05/4))^4t; A = 10,000(1 + (0.045/12))^12t
D. A = 25,000(1 + (0.05/4))^4t; A = 10,000(1 + (0.032/14))^12t
Question 11 of 40	2.5 Points

Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. log x + 3 log y

A. log (xy)
B. log (xy³)
C. log (xy²)
D. log_y (xy)³
Question 12 of 40	2.5 Points

Write the following equation in its equivalent exponential form. 5 = log_b 32

A. b⁵ = 32
B. y⁵ = 32
C. B^log5 = 32
D. Log^b = 32
Question 13 of 40	2.5 Points

Use the exponential growth model, A = A₀e^kt, to show that the time it takes a population to double (to grow from A₀ to 2A₀ ) is given by t = ln 2/k.

A. A₀ = A₀e^kt; ln = e^kt; ln 2 = ln e^kt; ln 2 = kt; ln 2/k = t
B. 2A₀ = A₀e; 2= e^kt; ln = ln e^kt; ln 2 = kt; ln 2/k = t
C. 2A₀ = A₀e^kt; 2= e^kt; ln 2 = ln e^kt; ln 2 = kt; ln 2/k = t
D. 2A₀ = A₀e^kt; 2 = e^kt; ln 1 = ln e^kt; ln 2 = kt; ln 2/k = t^oe
Question 14 of 40	2.5 Points

An artifact originally had 16 grams of carbon-14 present. The decay model A = 16e -0.000121t describes the amount of carbon-14 present after t years. How many grams of carbon-14 will be present in 5715 years?

A. Approximately 7 grams
B. Approximately 8 grams
C. Approximately 23 grams
D. Approximately 4 grams
Question 15 of 40	2.5 Points

Solve the following exponential equation. Express the solution set in terms of natural logarithms or common logarithms to a decimal approximation, of two decimal places, for the solution. e^x = 5.7

A. {ln 5.7}; 1.74
B. {ln 8.7}; 3.74
C. {ln 6.9}; 2.49
D. {ln 8.9}; 3.97
Question 16 of 40	2.5 Points

Evaluate the following expression without using a calculator. 8^log8 19

A. 17
B. 38
C. 24
D. 19
Question 17 of 40	2.5 Points

Use properties of logarithms to expand the following logarithmic expression as much as possible. Log_b (xy³/ z³)

A. 1/2 log_bx - 6 log_by + 3 log_bz
B. 1/2 log_b x - 9 log_b y - 3 log_b z
C. 1/2 log_b x + 3 log_b y + 6 log_b z
D. 1/2 log_b x + 3 log_b y - 3 log_b z
Question 18 of 40	2.5 Points

Evaluate the following expression without using a calculator. Log₇ 7

A. 1/4
B. 3/5
C. 1/2
D. 2/7
Question 19 of 40	2.5 Points

Write the following equation in its equivalent logarithmic form. 2^-4 = 1/16

A. Log₄ 1/16 = 64
B. Log₂ 1/24 = -4
C. Log₂ 1/16 = -4
D. Log₄ 1/16 = 54
Question 20 of 40	2.5 Points

Use properties of logarithms to condense the following logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. 3 ln x 1/3 ln y

A. ln (x / y^1/2)
B. ln_x (x⁶ / y^1/3)
C. ln (x³/ y^1/3)
D. ln (x^-3 / y^1/4)
Question 21 of 40	2.5 Points

Perform the long division and write the partial fraction decomposition of the remainder term. x⁴ x² + 2/x³ - x²

A. x + 3 - 2/x - 1/x² + 4x - 1
B. 2x + 1 - 2/x - 2/x + 2/x + 1
C. 2x + 1 - 2/x² - 2/x + 5/x - 1
D. x + 1 - 2/x - 2/x² + 2/x - 1
Question 22 of 40	2.5 Points

Solve each equation by the substitution method.

x + y = 1 x² + xy y² = -5

A. {(4, -3), (-1, 2)}
B. {(2, -3), (-1, 6)}
C. {(-4, -3), (-1, 3)}
D. {(2, -3), (-1, -2)}
Question 23 of 40	2.5 Points

Write the partial fraction decomposition for the following rational expression. x + 4/x²(x + 4)

A. 1/3x + 1/x² - x + 5/4(x² + 4)
B. 1/5x + 1/x² - x + 4/4(x² + 6)
C. 1/4x + 1/x² - x + 4/4(x² + 4)
D. 1/3x + 1/x² - x + 3/4(x² + 5)
Question 24 of 40	2.5 Points

Solve each equation by either substitution or addition method.

x² + 4y² = 20 x + 2y = 6

A. {(5, 2), (-4, 1)}
B. {(4, 2), (3, 1)}
C. {(2, 2), (4, 1)}
D. {(6, 2), (7, 1)}
Question 25 of 40	2.5 Points

Write the form of the partial fraction decomposition of the rational expression. 7x - 4/x² - x - 12

A. 24/7(x - 2) + 26/7(x + 5)
B. 14/7(x - 3) + 20/7(x² + 3)
C. 24/7(x - 4) + 25/7(x + 3)
D. 22/8(x - 2) + 25/6(x + 4)
Question 26 of 40	2.5 Points

Find the quadratic function y = ax² + bx + c whose graph passes through the given points. (-1, -4), (1, -2), (2, 5)

A. y = 2x² + x - 6
B. y = 2x² + 2x - 4
C. y = 2x² + 2x + 3
D. y = 2x² + x - 5
Question 27 of 40	2.5 Points

Write the partial fraction decomposition for the following rational expression. ax +b/(x c)² (c 0)

A. a/a c +ac + b/(x c)²
B. a/b c +ac + b/(x c)
C. a/a b +ac + c/(x c)²
D. a/a b +ac + b/(x c)
Question 28 of 40	2.5 Points

Solve the following system.

2x + 4y + 3z = 2 x + 2y - z = 0 4x + y - z = 6

A. {(-3, 2, 6)}
B. {(4, 8, -3)}
C. {(3, 1, 5)}
D. {(1, 4, -1)}
Question 29 of 40	2.5 Points

Write the partial fraction decomposition for the following rational expression. 6x - 11/(x - 1)²

A. 6/x - 1 - 5/(x - 1)²
B. 5/x - 1 - 4/(x - 1)²
C. 2/x - 1 - 7/(x - 1)
D. 4/x - 1 - 3/(x - 1)
Question 30 of 40	2.5 Points

Solve the following system.

x = y + 4 3x + 7y = -18

A. {(2, -1)}
B. {(1, 4)}
C. {(2, -5)}
D. {(1, -3)}
Question 31 of 40	2.5 Points

Solve the following system by the addition method. {2x + 3y = 6 {2x 3y = 6

A. {(4, 1)}
B. {(5, 0)}
C. {(2, 1)}
D. {(3, 0)}
Question 32 of 40	2.5 Points

Solve the following system.

2x + y = 2 x + y - z = 4 3x + 2y + z = 0

A. {(2, 1, 4)}
B. {(1, 0, -3)}
C. {(0, 0, -2)}
D. {(3, 2, -1)}
Question 33 of 40	2.5 Points

Let x represent one number and let y represent the other number. Use the given conditions to write a system of equations. Solve the system and find the numbers. The sum of two numbers is 7. If one number is subtracted from the other, their difference is -1. Find the numbers.

A. x + y = 7; x - y = -1; 3 and 4
B. x + y = 7; x - y = -1; 5 and 6
C. x + y = 7; x - y = -1; 3 and 6
D. x + y = 7; x - y = -1; 2 and 3
Question 34 of 40	2.5 Points

Write the partial fraction decomposition for the following rational expression. 1/x² c² (c 0)

A. 1/4c/x - c - 1/2c/x + c
B. 1/2c/x - c - 1/2c/x + c
C. 1/3c/x - c - 1/2c/x + c
D. 1/2c/x - c - 1/3c/x + c
Question 35 of 40	2.5 Points

Write the form of the partial fraction decomposition of the rational expression. 5x² - 6x + 7/(x - 1)(x² + 1)

A. A/x - 2 + Bx² + C/x² + 3
B. A/x - 4 + Bx + C/x² + 1
C. A/x - 3 + Bx + C/x² + 1
D. A/x - 1 + Bx + C/x² + 1
Question 36 of 40	2.5 Points

Many elevators have a capacity of 2000 pounds. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when x children and y adults will cause the elevator to be overloaded.

A. 50x + 150y > 2000
B. 100x + 150y > 1000
C. 70x + 250y > 2000
D. 55x + 150y > 3000
Question 37 of 40	2.5 Points

Solve the following system by the substitution method. {x + y = 4 {y = 3x

A. {(1, 4)}
B. {(3, 3)}
C. {(1, 3)}
D. {(6, 1)}
Question 38 of 40	2.5 Points

Perform the long division and write the partial fraction decomposition of the remainder term. x⁵ + 2/x² - 1

A. x² + x - 1/2(x + 1) + 4/2(x - 1)
B. x³ + x - 1/2(x + 1) + 3/2(x - 1)
C. x³ + x - 1/6(x - 2) + 3/2(x + 1)
D. x² + x - 1/2(x + 1) + 4/2(x - 1)
Question 39 of 40	2.5 Points

Solve the following system.

3(2x+y) + 5z = -1 2(x - 3y + 4z) = -9 4(1 + x) = -3(z - 3y)

A. {(1, 1/3, 0)}
B. {(1/4, 1/3, -2)}
C. {(1/3, 1/5, -1)}
D. {(1/2, 1/3, -1)}
Question 40 of 40	2.5 Points

Write the partial fraction decomposition for the following rational expression. x² 6x + 3/(x 2)³

A. 1/x 4 2/(x 2)² 6/(x 2)

B. 1/x 2 4/(x 2)² 5/(x 1)³

C. 1/x 3 2/(x 3)² 5/(x 2)

D. 1/x 2 2/(x 2)² 5/(x 2)³

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