Business Cal, Final Exam

8/11/2019 Business Cal, Final Exam

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Name:

Math 122 Final Exam

Directions: Please write your answers, with all appropriate work, in the spacesprovided. Answers given without work shown will be counted incorrect. You may usethe backs of the pages if you require some space for scratchwork or brainstorming.

All questions are worth 5 points.

1. Suppose that the value of a certain brand of otter plushie is modeled by the equationf(t) = 20 1

4t2, where t is the number of years since the initial run and f(t) is

given in dollars. What is the average rate of change in the price of the plushie fromt= 0 to t= 8 years?

2. Suppose that the supply and demand functions for magical clam-making devicesare, respectively, S(p) = 2p and D(p) = 1000 2p. Now suppose that a 10% salestax is placed upon consumers. Find the equilibrium price and quantity after the

imposition of the tax.

3. A radioactive super-otter has a half-life of 25 years. Write an exponential functiondescribing the amount of radioactive material left after tyears given that the otteris completely radioactive and weighs 10 pounds at t= 0.

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4. What is the present value of $1000 after 100 years in an account that yields 5%interest compounded quarterly?

5. Given the following table, estimate f(5):

x 4.7 4.8 4.9 5.0 5.1 5.2

f(x) 9.8 8.6 7.5 6.5 5.5 4.7

6. Take the derivative of each of the following expressions (with respect to x).

(a) x2ex+1

(b) 2x3 4

ln(x)

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(c) ln(7x2 + (x 1)10)

7. Find the tangent line to f(x) =x2 4 at x= 1.

8. Write a function r(x) describing the relative rate of change of the functionf(x) = ex

2

.

9. Given f(100) = 5 and f(100) = 2, estimate f(110).

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10. Suppose that the profit function for a company producing urchin minions is givenby (q) = q2 + 860q 164760. What is the maximum profit this company canachieve? How many minions do they need to sell to achieve this?

11. If an otters distance from Otter Dispatch is modeled by the equationP(t) = 10t t2 where t is in hours and P is in miles, what is the average ve-locity of the otter over a 5 hour trip? For what value oft is the actual velocity ofthe otter equal to this average velocity?

12. A rectangular fenced-in pen is being built along the edge of a river, as illustrated be-low. Given that the farmer has 100 feet of fencing available with which to construct

this pen, what dimensions will maximize the area?

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13. Given the cost function C(q) = q2 + 12q+ 25, for which value ofq is the averagecost minimized?

14. Estimate

2

0

x2 + 12xdxusing:

(a) a left Riemann sum with 4 subintervals.

(b) A right Riemann sum with 4 subintervals.

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Business Cal, Final Exam

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