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

log2 96 – log2 3

A. 5

B. 7

C. 12

2.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.

ex = 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

3.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

4.Solve the following logarithmic equation. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, to two decimal places, for the solution.

2 log x = log 25

A. {12}

B. {5}

C. {-3}

D. {25}

5.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

6.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. 7 grams

B. 8 grams

C. 23 grams

D. 4 grams

7.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 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, ∞)

8.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)

9.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

10.Solve the following system by the addition method.

{4x + 3y = 15

{2x – 5y = 1

A. {(4, 0)}

B. {(2, 1)}

C. {(6, 1)}

11.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)

D. {(3, 1)}

12.A television manufacturer makes rear-projection and plasma televisions. The proﬁt per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.

Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.

A. z = 200x + 125y

B. z = 125x + 200y

C. z = 130x + 225y

D. z = -125x + 200y

13.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)}

14.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)}

15.Solve the following system.

x = y + 4

3x + 7y = -18

A. {(2, -1)}

B. {(1, 4)}

C. {(2, -5)}

D. {(1, -3)}

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

16.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)}

C. {(1/3, 1/5, -1)}

D. {(1/2, 1/3, -1)}

17.Solve each equation by the substitution method.

y2 = x2 - 9

2y = x – 3

A. {(-6, -4), (2, 0)}

B. {(-4, -4), (1, 0)}

C. {(-3, -4), (2, 0)}

D. {(-5, -4), (3, 0)}

18.Write the partial fraction decomposition for the following rational expression.

1/x2 – c2 (c ≠0)

A. 1/4c/x

B. 1/2c/x - c - 1/2c/

C. 1/3c/x - c - 1/2c/x + c

D. 1/2c/x - c - 1/3c/x +

- 7 years ago

**ANSWERS (A+)**

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