algebra exam 5 - Norman93 only!!

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2.5 Points

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

A. 2 logb x + logb y - 2 logb z
B. 4 logb x - logb y - 2 logb z
C. 2 logb x + 2 logb y + 2 logb z
D. logb x - logb y + 2 logb z

Question 2 of 40

2.5 Points

Use the exponential growth model, A = A0ekt, 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 = A0ekt; ln = ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
B. 2A0 = A0e; 2= ekt; ln = ln ekt; ln 2 = kt; ln 2/k = t
C. 2A0 = A0ekt; 2= ekt; ln 2 = ln ekt; ln 2 = kt; ln 2/k = t
D. 2A0 = A0ekt; 2 = ekt; ln 1 = ln ekt; ln 2 = kt; ln 2/k = toe

Question 3 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 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. 31-x = 1/27

A. {2}

B. {-7}

C. {4}

D. {3}

Question 5 of 40

2.5 Points

Find the domain of following logarithmic function. f(x) = log5 (x + 4)

A. (-4, ∞)
B. (-5, -∞)
C. (7, -∞)
D. (-9, ∞)

Question 6 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. logy (xy)3

Question 7 of 40

2.5 Points

Write the following equation in its equivalent exponential form. 4 = log2 16

A. 2 log4 = 16
B. 22 = 4
C. 44 = 256
D. 24 = 16

Question 8 of 40

2.5 Points

Write the following equation in its equivalent exponential form. log6 216 = y

A. 6y = 216
B. 6x = 216
C. 6logy = 224
D. 6xy = 232

Question 9 of 40

2.5 Points

Use properties of logarithms to expand the following logarithmic expression as much as possible. logb (x2y)

A. 2 logy x + logx y
B. 2 logb x + logb y
C. logx - logb y
D. logb x – logx y

Question 10 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 11 of 40

2.5 Points

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

A. b5 = 32
B. y5 = 32
C. Blog5 = 32
D. Logb = 32

Question 12 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 13 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. ex+1 = 1/e

A. {-3}

B. {-2}

C. {4}

D. {12}

Question 14 of 40

2.5 Points

Consider the model for exponential growth or decay given by A = A0ekt. 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 15 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 16 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 17 of 40

2.5 Points

Find the domain of following logarithmic function. f(x) = log (2 - x)

A. (∞, 4)
B. (∞, -12)
C. (-∞, 2)
D. (-∞, -3)

Question 18 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 19 of 40

2.5 Points

Find the domain of following logarithmic function. f(x) = ln (x - 2)2

A. (∞, 2) ∪ (-2, -∞)
B. (-∞, 2) ∪ (2, ∞)
C. (-∞, 1) ∪ (3, ∞)
D. (2, -∞) ∪ (2, ∞)

Question 20 of 40

2.5 Points

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

A. 1/2 logb x - 6 logb y + 3 logb z
B. 1/2 logb x - 9 logb y - 3 logb z
C. 1/2 logb x + 3 logb y + 6 logb z
D. 1/2 logb x + 3 logb y - 3 logb z

Question 21 of 40

2.5 Points

Solve the following system by the addition method. {4x + 3y = 15 {2x – 5y = 1

A. {(4, 0)}

B. {(2, 1)}

C. {(6, 1)}

D. {(3, 1)}

Question 22 of 40

2.5 Points

Find the quadratic function y = ax2 + bx + c whose graph passes through the given points. (-1, 6), (1, 4), (2, 9)

A. y = 2x2 - x + 3
B. y = 2x2 + x2 + 9
C. y = 3x2 - x - 4
D. y = 2x2 + 2x + 4

Question 23 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 24 of 40

2.5 Points

Write the partial fraction decomposition for the following rational expression. 4/2x2 - 5x – 3

A. 4/6(x - 2) - 8/7(4x + 1)
B. 4/7(x - 3) - 8/7(2x + 1)
C. 4/7(x - 2) - 8/7(3x + 1)
D. 4/6(x - 2) - 8/7(3x + 1)

Question 25 of 40

2.5 Points

On your next vacation, you will divide lodging between large resorts and small inns. Let x represent the number of nights spent in large resorts. Let y represent the number of nights spent in small inns. Write a system of inequalities that models the following conditions: You want to stay at least 5 nights. At least one night should be spent at a large resort. Large resorts average $200 per night and small inns average $100 per night. Your budget permits no more than $700 for lodging.

y ≥ 1 x + y ≥ 5 x ≥ 1 300x + 200y ≤ 700

y ≥ 0 x + y ≥ 3 x ≥ 0 200x + 200y ≤ 700

y ≥ 1 x + y ≥ 4 x ≥ 2 500x + 100y ≤ 700

y ≥ 0 x + y ≥ 5 x ≥ 1 200x + 100y ≤ 700

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

Solve the following system.

x + y + z = 6 3x + 4y - 7z = 1 2x - y + 3z = 5

A. {(1, 3, 2)}
B. {(1, 4, 5)}
C. {(1, 2, 1)}
D. {(1, 5, 7)}

Question 28 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 29 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 30 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 31 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 32 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 33 of 40

2.5 Points

Solve each equation by the substitution method.

x2 - 4y2 = -7 3x2 + y2 = 31

A. {(2, 2), (3, -2), (-1, 2), (-4, -2)}

B. {(7, 2), (3, -2), (-4, 2), (-3, -1)}

C. {(4, 2), (3, -2), (-5, 2), (-2, -2)}

D. {(3, 2), (3, -2), (-3, 2), (-3, -2)}

Question 34 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 35 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 36 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 37 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 38 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

Question 39 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 40 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)}