Mathematics 7

Participation Exercises for MTH 125 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) ( - ) 1) _______

A) 36 - 6 B) 6 - 12 C) 54 D) 30

Rationalize the denominator. Assume that all variables represent positive real numbers.

2) 2) _______

A) B) 365 C) 4 D)

Simplify. Assume that all variables represent positive real numbers.

3) 3) _______

A) B) C) 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) Give the definition or an example of the phrase: Rationalizing the denominator. 7) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Express as a product.

8) 8) _______

A) b 3 B) 3 3 C) 3 D) b

Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables

represent positive real numbers.

9) ( 144 ∙ 227) 9) _______

A) 4 + 4 B) 144 + 227

C) 4 + 144 + 227 D) 32,688 + 32,688

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) x + y 10) ______

A) B) x y C) x ∙ y D) ( x + y)

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 6. 11) ______

A) 0.9030 B) 0.9542 C) 0.1436 D) 0.7781

Decide whether the statement is true or false.

12) = 6 + 6 12) ______

A) True B) False

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

13) Give a definition for the following term: quotient rule of logarithms. 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) 4x = 24 14) ______

A) { 1.792} B) { 6.000} C) { 2.292} D) { 0.436}

Solve the equation. Use natural logarithms. When appropriate, give solutions to three decimal places unless otherwise

indicated.

15) = 0.09 15) ______

A) { -29.547} B) { -22.149} C) { 14.164} D) { 17.72}

Solve the equation. Give the exact solution or solutions.

16) 9 = 5 16) ______

A) ∅ B) C) D)

Solve the problem.

17) Find the amount of money in an account after 6 years if $3900 is deposited at 4% annual interest compounded

quarterly. 17) ______

A) $4951.97 B) $4934.74 C) $4955.89 D) $4946.14

18) A sample of 700 grams of radioactive substance decays according to the function where t is the

time in years. How much of the substance will be left in the sample after 30 years? Round your answer to the nearest

whole gram. 18) ______

A) 0 g B) 2213 g C) 1 g D) 252 g

Provide an appropriate response.

19) The total number N of rabbits on a farmer's property, assuming unlimited resources and space, can be approximated

by the function N(x) = 50 , where x = 0 corresponds to the initial number of rabbits, and x = 1 corresponds to the

number of rabbits after one year, 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 3 months, there will be approximately 194 rabbits on the farm.

B) It means that with 194 rabbits on the farm, 3 new offspring will be born that year.

C) It means that after 3 years, there will be approximately 194 rabbits on the farm.

D) It means that after 3 years, there will be approximately 50 rabbits on the farm.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

20) When solving an exponential equation using logarithms, when is it easier to use natural logarithms?

20) _____________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Decide whether each function is one-to-one.

21) (i) f(x) = x2 - 4

(ii)

21) ______

A) (i) Yes; (ii) No B) (i) No; (ii) Yes C) (i) Yes; (ii) Yes D) (i) No; (ii) No