mth135

MTH 135 Homework Assignment Week 3 – July 28, 2021

Name___________________________________

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

Provide an appropriate response.

1) Find x to two decimal places.

x = 7,000 1) _______

A) 7813.95 B) 7831.95 C) 7975.01 D) 8320.50

2) Graph the function which calculates the present value of an amount of $5000 at an annual nominal rate of 7%

compounded continuously for 0 ≤ t ≤ 10. Use the formula P = A .

2) _______

A)

B)

C)

D)

3) A man with $9000 to invest puts the money into an account that earns 8% compounded continuously. Graph the

corresponding present value function and calculate the number of years before the $9000 will be due in order for its

present value to be $7000. Use the formula P = A .

3) _______

A)

3.14 years

B)

6.28 years

C)

0.84 years

D)

7.45 years

Solve the problem.

4) What will the value of an account (to the nearest cent) be after 8 years if $100 is invested at 6.0% interest compounded

continuously? 4) _______

A) $175.32 B) $161.61 C) $849.47 D) $159.38

5) How long will it take for the value of an account to be $890 if $350 is deposited at 11% interest compounded

continuously? Round your answer to the nearest hundredth. 5) _______

A) 0.93 yr B) 8.48 yr C) 10.41 yr D) 9.33 yr

6) Suppose that $8000 is invested at an interest rate of 5.5% per year, compounded continuously. How long would it take

to double the investment? 6) _______

A) 11.6 yr B) 12.6 yr C) 2 yr D) 13.6 yr

Find (x).

7) f(x) = 3 - 8x + 2 7) _______

A) 3 - 8x B) 3 - 6 C) 3x - 8 D) 3 - 8

8) f(x) = + 3 8) _______

A) 8 + B) 8 + 3x C) 8 + 3 D) 8x + 3

9) f(x) = -7 ln x - + 2 9) _______

A) - - 5x B) - 5 C) - - 5 D) - - 5

10) f(x) = ln - 3 10) ______

A) - 6x B) - 3x C) - 6x D) - 6x

11) f(x) = 3 ln x + ln + 4 11) ______

A) + 4x B) + 4 C) + + 4x D) + + 4

Use appropriate properties of logarithms to rewrite f(x), and then find (x).

12) f(x) = 5x + 4 ln 2x 12) ______

A) 5 + B) 5 + C) 5 + D) 7 +

Find for the indicated function y.

13) y = 7 x 13) ______

A) B) C) D)

14) y = 3 - x 14) ______

A) 6 + B) 3 - C) 6 - D) 6 -

15) y = -4 ln x + 7 x 15) ______

A) - + B) - + C) - + D) +

Find the equation of the line tangent to the graph of f at the indicated value of x.

16) f(x) = 2 ; x = 0 16) ______

A) y = 2x B) y = x + 2 C) y = 2x - 2 D) y = 2x + 2

17) f(x) = 8 + ln x; x = 1 17) ______

A) y = x - 9 B) y = x + 9 C) y = x - 7 D) y = x + 7

Provide an appropriate response.

18) Use graphical approximation methods to find the point(s) of intersection of f(x) = and g(x) = to two decimal

places. 18) ______

A) (-0.87, 0.42), (1.23, 3.41) B) (1.23, 3.41)

C) (0.87, 0.42), (1.23, 3.41) D) (-0.87, 0.42)

Solve.

19) The salvage value S (in dollars) of a company airplane after t years is estimated to be given by

What is the rate of depreciation (in dollars per year) after 5 years? 19) ______

A) -$ 42,018/yr B) -$ 14,987/yr C) -$ 67,625/yr D) -$ 21,409/yr

20) A single bacterium divides every 0.5 hour to produce two complete bacteria. If we start with a colony of 6000 bacteria,

after t hours there will be bacteria. Find A'( 5). 20) ______

A) 8,517,393 bacteria B) 133,084 bacteria

C) 2,129,348 bacteria D) 34,069,570 bacteria

Differentiate.

21) Find f'(t) for f(x) = ( 3x - 4)( 4x3 - x2 + 1) 21) ______

A) f'(x) = 48x3 - 19x2 + 57x + 3 B) f'(x) = 12x3 + 19x2 - 57x + 3

C) f'(x) = 48x3 - 57x2 + 8x + 3 D) f'(x) = 36x3 + 57x2 - 19x + 3

22) Find f'(x) for f(x) = (5 + 4)(3 - 5). 22) ______

A) f'(x) = 150 + 84 - 75 B) f'(x) = 20 + 84 - 75

C) f'(x) = 150 + 84 - 75x D) f'(x) = 20 + 84 - 75x

23) Find f'(t) for f(x) = . 23) ______

A) - B) C) D) -

24) Find for y = . 24) ______

A) = B) =

C) = D) =

Provide an appropriate response.

25) Find the derivative of the function at 25) ______

A) B) - C) D) -

26) Find the values of x where the tangent line is horizontal for the graph of 26) ______

A) x = 0, x = -2 B) x = 0, x = -4

C) x = -2 D) x = -2, x = 0, x = -4

Solve the problem.

27) One hour after x milligrams of a particular drug are given to a person, the change in body temperature T(x), in

degrees Celsius, is given approximately by:

T(x) = - , 0 ≤ x ≤ 6

Find the sensitivity, T'(x), of the body to a dosage of three milligrams. 27) ______

A) - degrees per mg B) - degrees per mg

C) degrees per mg D) degrees per mg