Mathematics, 21.02.2020 00:40 Levantine2643
The quantity demanded per month, x, of a certain make of personal computer (PC) is related to the average unit price, p (in dollars), of PCs by the equationx = f(p) =1009810,000 − p2It is estimated that t mo from now, the average price of a PC will be given byp(t) =4001 +18t+ 200 (0 ≤ t ≤ 60)dollars. Find the rate at which the quantity demanded per month of the PCs will be changing 16 mo from now. (Round your answer to one decimal place.)
Answers: 2
while the rate of change of quantity demanded per month after 16 months is 18.7.
![\frac{dx}{dp}=\frac{d(\frac{100}{9}\sqrt{810000-p^2})}{dp}\\\frac{dx}{dp}=\frac{100}{9}\frac{d}{dp}[(810000-p^2)^{1/2}]\\\frac{dx}{dp}=\frac{100}{9}\frac{1}{2}[(810000-p^2)^{-1/2}]\frac{d}{dp}[(810000-p^2)]\\\frac{dx}{dp}=\frac{50}{9}[(810000-p^2)^{-1/2}](-2p)\\\frac{dx}{dp}=\frac{100p}{9\sqrt{(810000-p^2)}}](/tpl/images/0518/3935/780d4.png)
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