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

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Christiana Veronica Preston
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1 Assn.1-.3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) 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. A) 9.33 yr 0.93 yr C) 10.1 yr D) 8.8 yr 2) Radioactive carbon-1 has a continuous compound rate of decay of r = Estimate the age of a skull uncovered at an archaeological site if 6% of the original amount of carbon-1 is still present. (Compute answer to the nearest year.) A) 22,689 yr 12,027 yr C) 70 yr D) 20,032 yr 1) 2) 3) Find t to four decimal places. e-t = 0.06 A) C) D) ) ) If $5000 is invested at 5.25% compounded continuously, what is the amount in the account after 10 years? A) $ $ C) $ D) $ ) 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? A) $ $ C) $ D) $89.7 6) An investor buys 100 shares of a stock for $20,000. After 5 years the stock is sold for $32,000. If interest is compounded continuously, what annual nominal rate of interest did the original $20,000 investment earn? (Represent the answer as a percent to three decimal places.) A) 0.09% 9.00% C) 1.200% D) 8.70% ) 5) 6) 7) 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 = Ae-rt. 7) 1

2 A) 6.28 years C) 0.8 years D) 3.1 years 7.5 years 8) 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? A) 13.6 yr 2 yr C) 12.6 yr D) 11.6 yr 8) 9) Find x to two decimal places. x = 7,000e0.11 A) C) D) ) 10) Find: lim 5000e-0.07t 10) x A) 0 C) 5000 D) 1 Find the equation of the line tangent to the graph of f at the indicated value of x. 11) f(x) = 3ex - 1; x = 0 11) A) y = 2x + 2 y = 3x - 2 C) y = 3x + 2 D) y = 3x + 3 2

3 Find f (x). 12) f(x) = 8ex + ln x3 12) A) 8ex ex + 12 C) 8ex + D) 8ex + 12 x3 x2 x2 x 13) f(x) = ln x3 - x2 13) 3 A) x2-8x 1 3x - 8x C) 3 x - 8x D) 3 x - x 1) The resale value R (in dollars) of a company car after t years is estimated to be given by R(t) = 22,500(0.8)t. What is the rate of depreciation (in dollars per year) after 3 years? A) -$1953/yr -$2325/yr C) -$161/yr D) -$1,651/yr 1) Find f (x). 15) f(x) = 7ex - 6x ) A) 7ex - 7ex - 6x C) 7xex-1-6 D) 7ex ) 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 A(t) = t = 6000 t bacteria. Find A'(5). A) 2,129,38 bacteria 3,069,570 bacteria C) 8,517,393 bacteria D) 133,08 bacteria 16) Find dy dx for the indicated function y. 17) y = x - x 17) A) 8x3 - ln 8x3 - x ln C) 8x3 - x ln x D) 8x3 + x ln 18) The salvage value S (in dollars) of a company airplane after t years is estimated to be given by S(t) = 250,000(0.7)t. What is the rate of depreciation (in dollars per year) after 3 years? A) -$3,693/yr -$9,206/yr C) -$85,750/yr D) -$30,585/yr 18) Find f (x). 19) f(x) = -ex + 7x - 19) A) -xex ex + 7x C) -ex + 3 D) -ex + 7 Find the equation of the line tangent to the graph of f at the indicated value of x. 20) f(x) = 2 + ln x5; x = e 20) A) y = 5x e + 2 y = 5x C) y = 5x e e - 2 D) y = 5x e + 7 3

4 21) A publishing company has published a new magazine for young adults. The monthly sales S (in thousands) is given by S(t) = 800t, where t is the number of months since the first issue was t + 2 published. Find S(3) and S'(3) and interpret the results. A) At three months, the monthly sales are $2, 00,000 and increasing at 6,000 magazines per At three months, the monthly sales are $80,000 and decreasing at 6,000 magazines per C) At three months, the monthly sales are $80,000 and increasing at 6,000 magazines per D) At three months, the monthly sales are $2,00,000 and increasing at 800,000 magazines per 21) 22) Find f'(t) for f(x) = (2x - 5)(x3 - x2 + 1) 22) A) f'(x) = 2x3 + 66x2-22x + 2 f'(x) = 32x3-66x2 + 10x + 2 C) f'(x) = 32x3-22x2 + 66x + 2 D) f'(x) = 8x3 + 22x2-66x ) Find the derivative of the function f(x) = 2x - 7 at x = 2. 23) 3x - 2 A) C) - 17 D) ) Find dy dx for y = x 3 x ) A) dy dx = 2x 3-3x2 C) dy dx = -2x 3-3x2 dy dx = 2x 3 + 3x2 D) dy dx = - 2x 3 + 3x2 25) Find the values of x where the tangent line is horizontal for the graph of f(x) = x 2 x ) A) x = -2 x = -2, x = 0, x = - C) x = 0, x = -2 D) x = 0, x = - 26) Find dy dx for y = x 2-3x ) x7-2 A) dy dx = - 5x x7-13x6 - x + 6 (x7-2) 2 dy dx = - 5x x7-1x6-3x + 6 (x7-2) 2 C) dy dx = - 5x x7-1x6 - x + 6 (x7-2) 2 D) dy dx = - 5x x7-1x6 - x + 6 (x7-2) 2

5 27) Find dy dx for y = -5x 3-5x Do not simplify. 27) -5x + 2 A) (-5x + 2)(-15x2-10x) - (-5x3-5x2 + 3)(-20x3) (-5x + 2) 2 C) (-5x3-5x2 + 3)(-20x3) - (-5x + 2)(-15x2-10x) (-5x3-5x2 + 3) 2 (-5x3-5x2 + 3)(-20x3) - (-5x + 2)(-15x2-10x) (-5x + 2) 2 D) (-5x + 2)(-15x2-10x) - (-5x3-5x2 + 3)(-20x3) (-5x3-5x2 + 3) 2 28) Find f'(x) for f(x) = (5x3 + )(3x7-5). 28) A) f'(x) = 150x9 + 8x6-75x f'(x) = 150x9 + 8x6-75x2 C) f'(x) = 20x9 + 8x6-75x D) f'(x) = 20x9 + 8x6-75x2 29) Find f'x for f(x) = (3x + ) 2. Do not simplify. 29) x3 - x2 + 3x A) 6(x3 - x2 + 3x)(3x + ) - (3x + )2(3x2-2x + 3) (3x + ) (3x + ) 2(3x2-2x + 3) - 6(x3 - x2 + 3x)(3x + ) (x3 - x2 + 3x) 2 C) 6(x 3 - x2 + 3x)(3x + ) - (3x + )2(3x2-2x + 3) (x3 - x2 + 3x)2 D) (3x + ) 2(3x2-2x + 3) - 6(x3 - x2 + 3x)(3x + ) (3x + ) 30) Find f'(t) for f(x) = x 5x ) A) - 8 5x x - 8 C) - 8 D) - 8x 5

Instructor: Elhoussine Ghardi Course: calcmanagementspring2018

Student: Date: Instructor: Elhoussine Ghardi Course: calcmanagementspring018 Assignment: HW3spring018 1. Differentiate the following function. f (x) = f(x) = 7 4x + 9 e x. f(x) = 6 ln x + 5x 7 3. Differentiate