Answer
p=$50 - 3x^{\frac{2}{3}}$
Work Step by Step
R(x)= $\int (50 - 5x^{\frac{2}{3}})dx$
= $50x - 3x^{\frac{5}{3}} + C$
To find the C, we know R(0)=0 since if no items are sold, the revenue is 0. So:
$0 = 50(0)- 3(0)^{\frac{5}{3}} + C$
$C = 0$
Thus, the revenue function is: R(x) = $50x - 3x^{\frac{5}{3}}$
Recall that R= qp, where p is the demand function giving the price p as a function of q. Then
$50x - 3x^{\frac{5}{3}} = xp$
$\frac{50x - 3x^{\frac{5}{3}}}{x} = p$
The demand function is p=$50 - 3x^{\frac{2}{3}}$
