Math

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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.

  • Math -

    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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