Mathematics 7
MTH 125 Homework Assignment for Week 7
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Multiply, then simplify the product. Assume that all variables represent positive real numbers.
1) ( + 5)( – 3) 1) _______
A) – 3 + 5 – 15 B) – 15
C) + 2 – 15 D) 3 – 15
Rationalize the denominator. Assume that all variables represent positive real numbers.
2) – 2) _______
A) – B) – C) -8 D) -7
Simplify. Assume that all variables represent positive real numbers.
3) 3) _______
A) B) C) 7 D)
Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is
not zero.
4) 4) _______
A) B) C) D)
Write the expression in lowest terms. Assume that all variables represent positive real numbers.
5) 5) _______
A) B) C) D)
Rationalize the numerator. Assume that all variables represent positive real numbers.
6) 6) _______
A) B) C) D)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
7) Tell whether the statement is true or false. If it is false, give the correct answer. Explain your answer. Assume that x
represents a positive real number. 7) _____________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Express as a product.
8) 8) _______
A) 5 2 B) 5 C) 2 2 D) 2
Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables
represent positive real numbers.
9) 9) _______
A) 8 – 7 B) 7 ÷ 8
C) 7 – 8 D) 7 + 7
Rewrite the given expression as a single logarithm. Assume that all variables are defined in such a way that variable
expressions are positive and bases are positive numbers not equal to 1.
10) 6 + r 10) ______
A) (6 + r) B) C) 6 ∙ r D) 6 r
Evaluate the given logarithm by applying the appropriate rule(s). DO NOT USE A CALCULATOR.
11) Given 2 = 0.3010 and 3 = 0.4771, evaluate 72. 11) ______
A) 1.8572 B) 0.8616 C) 0.2549 D) 2.0333
Decide whether the statement is true or false.
12) ( 7 – 15) = 7 – 15 12) ______
A) False B) True
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
13) A student claims that since x = a is not defined for negative values of x, then a must also not be negative. What is
wrong with this statement? 13) _____________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the equation. Give the solution to three decimal places.
14) 3 x – 2 = 11 14) ______
A) { 0.183} B) { 3.299} C) { 5.667} D) { 4.183}
Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise
indicated.
15) = 28 15) ______
A) { 7.228} B) { 1.536} C) { 3.332} D) {0. 138}
Solve the equation. Give the exact solution or solutions.
16) ( 8x – 3) = 2 16) ______
A) { 4} B) C) D)
Solve the problem.
17) Find the amount of money in an account after 3 years if $3300 is deposited at 6% annual interest compounded
semiannually. 17) ______
A) $3949.05 B) $3940.37 C) $3945.54 D) $3930.35
18) How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to
the function A(t) = , where t is the time in years? Round your answer to the nearest hundredth year.
18) ______
A) 23.50 yr B) 26.45 yr C) 58.75 yr D) 2.95 yr
Provide an appropriate response.
19) The total number N of bacteria cells in a petri dish when exposed to a new drug can be approximated by the function
N(x) = 75 , where N is measured in thousands; and x = 0 corresponds to the initial number of cells, x = 1
corresponds to the number of cells after one hour, and so on. The function is graphed on a graphing calculator-generated
screen. Interpret the meanings of x and y in the display at the bottom of the screen.
19) ______
A) It means that after 75 hours, there will be approximately 45,200 bacteria cells.
B) It means that the drug is helping the bacteria grow.
C) It means that after 20 hours, there will be approximately 45,200 bacteria cells.
D) It means that after 20 hours, there will be approximately 45 bacteria cells.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the que stion.
20) When solving an exponential equation using logarithms, when is it easier to use common logarithms?
20) _____________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find (x) for the one-to-one function f(x) shown.
21) f(x) = 21) ______
A) (x) = + 5 B) (x) = – 5 C) (x) = + 5 D) (x) = – 5
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