# IUB BUEX-C 531 - MATH 201. Test Review 3 (5 pages)

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**View the full content.**## MATH 201. Test Review 3

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## MATH 201. Test Review 3

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- Pages:
- 5
- School:
- Indiana University, Bloomington
- Course:
- Buex-C 531 - Introduction to Business Analytics

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MATH 201 Brief Calculus Review for Test 3 1 Find the number of units x that produces a maximum revenue 2 a R 500 x x b R 60 x 2 3 4x 2 Find the number of units x that produces minimum average cost per unit Round to the nearest whole unit C 0 12 x 2 15 x 3000 3 Find the price that will maximize profit for the demand and cost function where p is the price in dollars x is the number of units and C is the cost in dollars a p 80 x C 150 20 x b p 50 0 1 x C 35 x 500 4 5 a Find the amount s spent on advertising in thousands of dollars that maximizes the profit P in thousands of dollars b Find the point of diminishing returns 6 7 Simplify the expressions 4 3 12 5 5 a 2e5 3 b e 8 Sketch the graph of the following functions x x a f x 5 b g x 3e c 16 e 0 13 12 9 a Use the model to estimate the sales in 2010 b Use the model to estimate the sales in 2018 10 The current price of a car wash is 15 Use the model to estimate the price of a car wash in 10 years 11 On the day of a child s birth 500 is deposited in an account that pays 6 interest compounded continuously Determine the balance in this account on the child s 21 st birthday n r reff 1 1 n find the effective rate corresponding 12 Given the formula for the effective rate of interest to a nominal rate of 8 2 compounded a annually b semi annually c quarterly d monthly 13 How much should be deposited now in an account paying 9 5 compounded quarterly in order to have a balance of 25000 in 15 years 14 The average time between incoming calls at a switchboard is 3 minutes If a call has just come in the probability that the next call will come within the next t minutes is t P t 1 e 3 Find the probability of each situation a A call comes within minute b A call comes within 2 minutes 15 The cost of producing x units of a product is modeled by C 120 45 x 150 ln x x 1 a Find the average cost function C b Find the number of units that will give a minimum average cost Round your answer to the nearest whole unit 16 Differentiate each of the functions x x a g x 3e b g x e 5e x f x x d x c h x 2e 2 3 x e h x 2 xe x 17 Write the equation of the line tangent to f x e 1 at the point 0 2 18 19 Solve for x Round your answers to two decimal places a 2x 4 e 12 b ln x 5 c 1 6 3 x 7 20 The population P in thousands of Phoenix Arizona from 1980 to 2009 can be modeled by P 788 e 0 0248t where t 0 corresponds to 1980 a What was the population in 2007 b When will the population likely reach 3 000 000 21 Find the derivative of each of the following functions a f x ln 4 x 1 b y 53 x 7 c y 2 xln x 22 Find an equation of the tangent line to the graph of f x ln x 2 at the point 1 0 Answers 1a 250 units b 1000 units 2 158 units 3a 50 3b 40 4a 75 4b 50 75 per unit 5a 10 000 5b 5833 33 6 1312 50 1 10 7a 5 8a 1 9765625 7b 2e8 7c 16e1 56 8b 9a 73 13 billion b 187 63 billion 10 22 20 11 1762 71 12a 8 2 b 8 3681 c 8 4556 d 8 5153 13 6113 71 14a 0 1535 15a C b 0 4866 150 ln x 120 45 x x x 16a 3e 17 y x 2 b 20 21 per unit x c 4 xe x b e 2 5e x x 1 x2 d 3 18a 433 31 per year b 890 22 per year c 21839 26 per year 19a 0 55 b 148 41 c 20a 1 539 323 b in 2033 or 2034 21a 4 4 x 1 b 3 ln 5 53 x 7 e 1 38 c 2 2 ln x 2e x x 1 22 y 2x 2

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