Answer
p=$\frac{600x - 25000e^{0.0002x} + 25000}{x} $
Work Step by Step
R(x)= $\int (600 - 5e^{0.0002x})dx$
= $600x - 25000e^{0.0002x} + C$
To find the C, we know R(0)=0 since if no items are sold, the revenue is 0. So:
$0 = 600(0)- 25000e^{0.0002*0} + C$
$C = 25000$
Thus, the revenue function is: R(x) = $600x - 25000e^{0.0002x} + 25000$
Recall that R= qp, where p is the demand function giving the price p as a function of q. Then
$600x - 25000e^{0.0002x} + 25000= xp$
$\frac{600x - 25000e^{0.0002x} + 25000}{x} = p$
The demand function is p=$\frac{600x - 25000e^{0.0002x} + 25000}{x} $
