How do I find the rate of change of the revenue?

Question

The price p (in dollars) and demand x (in bushels) for peaches are related by

x=6500-0.15p^2

If the current price of $90 per bushel is decreasing at the rate of $5 per week, find the rate of change (in collars per week) of the revenue.

The answer is -14,275 according to my professor but I have not been able to get that. I know you have to find the revenue equation from the price and demand one [R(x)=demand * price] -> [R(x)=x*p] but I am finding it difficult as p is squared. Can someone write out the steps to solve this?

Answer 1

I assume you are taking calculus...if not, I am not sure how to advise you.

Revenue = px = 6500p - .15p³

the derivative dR/dt = 6500 - 4.5p² dp/dt

Now just plug in the values you have for p and dp/dt.