# m116q07a - 1 c [email protected] MATHA116 Survey of Calculus...

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1 MATHA116, Survey of Calculus, Quiz #7 Solutions Updated on November 8, 2006 Get help whenever in doubt! c [email protected] D irection. IX-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 IX-1. ( 40 points ) The demand equation for a certain brand of metal alloy audiotape is 100 x 2 + 9 p 2 = 3600 where x represents the number (in thousands) of ten-packs demanded each week when the unit price is p (in dollars). How fast is the quantity demanded increasing when the unit price/ten- pack is \$14 and the selling price is dropping at the rate of \$0 . 15/ten-pack/week? W ork IX-1. From the information given, we know that when p = 14 and dp dt = - 0 . 15, x can be found as shown below. 100 x 2 + 9 p 2 = 3600 = 100 x 2 + 9 · 14 2 = 3600 (1) x 2 = 3600 - 9 · 14 2 100 = x = r 3600 - 9 · 14 2 100 4 . 2849 (2) Now, the question here is to find dx dt where t is time in weeks.

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