Math

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. p(25) =

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  1. dp/dx = kp

    points on p(X): (0,100) ; (8;60.83)

    dp/dx= kp

    dp/p= kdx

    ln(p)=kx + c

    ln(100)=k(0) + c
    4.6=c
    ln(60.83)=8k + 4.6
    k= -0.0614

    ln(p)=-.0614*25+4.6
    ln p= 3.063
    p= 21.39 at x=25

    check my thinking.

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    bobpursley

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