Math
posted by Jules on .
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) =

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.