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# m116q05a - 1 c [email protected] MATHA116 Survey of Calculus...

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1 MATHA116, Survey of Calculus, Quiz #5 Solutions Updated on October 10, 2006 Get help whenever in doubt! c [email protected] D irection. VII-1. Please read each of the following questions carefully. Show your work as much as possible. No partial credit will be given without proper work shown. Write your answer above the Answer line. Use the back of each page should more space be needed. N Important: Direction. Q uestion VII-1. ( 40 points ) A study prepared for the Sunbelt town’s cham- ber of commerce projected that the town’s population in the next three years will grow according to the rule P ( t ) = 50000 + 30 t 3 / 2 + 20 t , where P ( t ) denotes the population t months from now. How fast will the population be increasing nine months from now? W ork VII-1. We need to calculate P 0 (9). P 0 ( t ) = 50000 + 30 t 3 / 2 + 20 t · 0 = sum rule z }| { (50000) 0 + 30 t 3 / 2 · 0 + (20 t ) 0 (1) = constant multi. rule z }| { 0 + 30 t 3 / 2 · 0 + 20 ( t ) 0 = power rule z }| { 30 3 2 t 3 / 2 - 1 + 20 (1) (2) = 45 t + 20 , = (3) P 0 (9) = 45 p (9) + 20 = 45 · 3 + 20 = 155 . (4) That is, the population will be increasing at a pace of 155 people per month 9 months from now.

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m116q05a - 1 c [email protected] MATHA116 Survey of Calculus...

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