Assignments: MA240 Online Exam 5

Question 1 of 40

5.0 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 2 of 40

5.0 Points

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
D. 4

Question 3 of 40

5.0 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

5.0 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 5 of 40

5.0 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 6 of 40

5.0 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 7 of 40

5.0 Points

Evaluate the following expression without using a calculator.

8^log8 19

A. 17
B. 38
C. 24
D. 19

Question 8 of 40

5.0 Points

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

e^-0.95

A. .483
B. 1.287
C. .597
D. .387

Question 9 of 40

5.0 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 10 of 40

5.0 Points

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}

Question 11 of 40

5.0 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 12 of 40

5.0 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 13 of 40

5.0 Points

Find the domain of following logarithmic function.

f(x) = ln (x - 2)²

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

Question 14 of 40

5.0 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 15 of 40

5.0 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 16 of 40

5.0 Points

Find the domain of following logarithmic function.

f(x) = log (2 - x)

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

Question 17 of 40

5.0 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 18 of 40

5.0 Points

Write the following equation in its equivalent exponential form.

log₆ 216 = y

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

Question 19 of 40

5.0 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 20 of 40

5.0 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.

3^2x + 3^x - 2 = 0

A. {1}
B. {-2}
C. {5}
D. {0}

Question 21 of 40

5.0 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 22 of 40

5.0 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 23 of 40

5.0 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 24 of 40

5.0 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 25 of 40

5.0 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 26 of 40

5.0 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 27 of 40

5.0 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 28 of 40

5.0 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) Incorrect
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 29 of 40

5.0 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.


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

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

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

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

Question 30 of 40

5.0 Points

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

Question 31 of 40

5.0 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 32 of 40

5.0 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 33 of 40

5.0 Points

Solve each equation by the addition method.

x² + y² = 25
(x - 8)² + y² = 41

A. {(3, 5), (3, -2)}
B. {(3, 4), (3, -4)}
C. {(2, 4), (1, -4)}
D. {(3, 6), (3, -7)}

Question 34 of 40

5.0 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 35 of 40

5.0 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 36 of 40

5.0 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 37 of 40

5.0 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

5.0 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.