Math
posted by Jules .
Could someone work this question out so I understand it. Thanks
The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of $100 per unit [p(0)=100], and there is a weekly demand of 8 units at the price of $60.83 per unit [p(8)=60.83].
A)find the price demand equation. Give an exact answer in simplified form. Round all decimal values to the nearest hundreth.
B)At a demand of 25 units per week, what is the price? Round to the nearest cent.

dp/dx = k p
dp/p = k dx
ln p = kx + C
p = e^(kx+C) = c e^kx
p(0)= + 100
so
100 = c e^0 = c
so
p = 100 e^kx
p(8) = 60.83
60.83 = 100 e^(k*8)
ln(.6083) = 8 k
k = .06214
so
p = 100 e^(.06214 x)
if x = 25
p = 100 e^(.0214*25)
p = 100 * .5857
p = $58.57
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