Part I Show All Your Work

MAT170 – Precalculus EXAM 2 Firoz

MAT 170 - Precalculus
EXAM #2
Dr Firozzaman March 29-30

PART I – Free response. Show all your work.

Make sure that you have 7 questions in the firsr part and 10 questions in the second part.

1. a. Find the accumulated value of an investment of $5000 at rate of interest of 5% compounded monthly for 8 years. [5 pts.]

Solution: A = 7452.93

b. What initial investment at 6% interest compounded continuously for seven years will accumulate to $50,000? Round your answer to the nearest cent. [5 pts.]

2. a. Use the properties of logarithms to expand the logarithmic expression as much as possible. [4 pts.]

b. Use the properties of logarithms to condense the logarithmic expression as much as possible.

[4 pts.]

3. Algebraically solve the following equations for x. [12 pts.]

a. .

Solution:

b. . Where

Thus

4. In 2000, the population of the U.S.A. was approximately 281.4 million people, and by 2003 it was 294.0 million people. Use the exponential growth model , in which t is the number of years after 2000, to find: [10 pts.]

a. an exponential function that models this growth.

b. Use this model to predict in what year the population of the U.S.A. will reach 360 million people.

5. Given that and t is in quadrant II. Find the following: [12 pts.]

6. A plane is flying at an elevation of 34,000 ft. The pilot finds that the angle of depression to “A” Mountain at ASU is . [10 pts.]

a.) Find the distance between the plane and “A” Mountain.

b) Find the distance between a point on the ground directly below the plane and “A” Mountain.

7. a) Given that, what is the range of [4 pts.]

b) Given that, what is [4 pts.]

PART II – Multiple choice. Chose the response that best completes the statements or answers the question. Write the letter on the blank line. Use capital block letters A, B, C, D, E. Each problem is worth 3 points.

____B___1. Find the domain of the logarithmic function .

A. B. C. D. E. None of these

____C___2. Write the equation in its equivalent exponential form: .

A. B. C. D. E. None of these

____C___3. Suppose and. Then the exact value of is

A. B. C. D. E. None of these

___D____4. The domain of is:

A. {x |, n is an integer} B. {x |, n is an integer}

C. D. {x |, n is an integer}

E. None of these

___B____5. Convert the angle 54° to radians. Express your answer as a multiple of π.

A. radians B. radians C. radians D. radians E. None of these

___B___6. Find the length of arc on a circle with radius inches intercepted by a central angle

, round your answer to two decimal places.

A. 15.6 inches B. 17.45 inches C. 18.74 inches D. 19.88 inches E. None of these

____D__7. What is the range of the cosine function?

A. B. (–1, 1) C. D. [–1, 1] E. None of these.

____A__8. Given , find the period:

A. B. C. D. E. None of these.

___C___9. Given , find the phase shift:

A. B. C. D. E. None of these.

___B__10. Find the equation for the graph below.

A. B.

C. D.

E. None of these