Trouble with revenue function

[root_beer]

This problem has 3 parts but basically if anyone can help me figure out the revenue function i should be able to figure out the rest.

Here is the problem:
For the next five years the price of a certain bike is predicted to vary according to p(t)=300-30t+7.5t^2, where t is time in years and p(t) is price in dollars. Number of bikes sold annually at the shop is expected to follow q(t)=3000+90t-15t^2, where q(t) is the number sold and t is time in years.

So i am trying to figure out the revenue function, any and all help will be greatly appreciated. Thanks.

 

[Gene]

Unless I'm missing something
revenue = price*quantity =p(t)*q(t)
but that is algebra, not calculus.

 

[root_beer]

is that all there is to it? i dont need to use the product rule or anything?
thanks for the help.

 

[Gene]

I could be wrong, but to my mind you use the product rule when you can't or don't want to multiply the terms out or you don't know the derivitive. Like x*e^x. The derivitive of a product is not the product if the derivitives but I don't see why, if you have formed the product, the derivitive that product would be different than if you used the product rule on the factors. The derivitive of x^2+x =
(2x+1)*dx
The derivitive of x(x+1) =
x*dx+(x+1)*dx =
(2x+1)*dx

If I'm wrong some of the brains will jump all over me.