t4(5) - (2 ²or the demand function q = 225 e 10 p 2 Fnd E...

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Methods of Calculus, Test 4E April 22, 2002 Instructions: Write your complete solutions in your exam book. Do not write on this paper. This is a closed-book test. No calculators are allowed to be used. To receive credit, you must show all work. Some numerical answers may involve the function ln or the number e . You are not required to simplify your answers. (1) Approximately 10,000 bacteria are placed in a culture. Let P ( t ) be the number of bacteria present in the culture after t hours, and suppose that P ( t ) satisFes the di±erential equation P 0 ( t ) = 0 . 55 P ( t ) . (a) ²ind the formula for P ( t ). (b) How many bacteria are there after 5 hours? (c) At what time will the size of the culture double? (d) How fast is the bacteria culture growing when it reaches 100,000?
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Unformatted text preview: (2) ²or the demand function q = 225 e-. 10 p 2 , Fnd E ( p ) and determine if demand is elastic or inelastic when p = 2 (3) ²ind the antiderivative Z ± √ x-3 e x-5 x ² dx (4) Integrate Z 4 1 x-1 / 2 dx (5) A company’s marginal cost function is MC ( x ) = 3 x 2-12 x + 12 where x is the production level. If the Fxed costs are 10, Fnd the cost function. (6) The marginal proFt function is MP ( x ) = 100 x 2 . ²ind the extra proFt earned from the sale of 2 additional units if 9 units are currently being produced. (7) ²ind the area of the region bounded by the curves y = 1 + 2 x-x 2 and y = 2 x-3....
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This note was uploaded on 07/13/2011 for the course MAC 2233 taught by Professor Staff during the Spring '08 term at FAU.

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