Mathematics, 13.07.2020 21:01 jself
Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average unit price, p (in dollars), of tablet computers by the equation x = f(p) = 100 9 810,000 − p2 It is estimated that t months from now, the average price of a tablet computer will be given by p(t) = 400 1 + 1 8 t + 200 (0 ≤ t ≤ 60) dollars. Find the rate at which the quantity demanded per month of the tablet computers will be changing 25 months from now. (Round your answer to one decimal place.) tablet computers/month
Answers: 1
![\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}](/tpl/images/0704/1987/4a557.png)
![\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}](/tpl/images/0704/1987/0bc75.png)
![\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]](/tpl/images/0704/1987/757ec.png)
![\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009](/tpl/images/0704/1987/9f410.png)
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Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer...
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