Can i get someone to check my work, this question is about composite functions?

Question

A firm has a revenue function given by R(p) = 10p - p^2, where p is the price of a chocolate bar sold in dollars and "R" is measured in thousands of dollars per day. Suppose the firm is able to increase the price of each bar by 5 cents each year (without affecting demand). If "t" is time measured in years, write an equation for the revenue as a function of t if the price of candy bar starts out at 25 cents.

This is the revenue function. R(p) = 10p - p^2.

P(t) = .25 +.05(t) <This is what i got out of " write an equation for the revenue as a function of t if the price of a candy bar starts out at 25 cents"

So R(t) = R(t(p) = 10p - 2p(.25 +.05(t))^2 ????

R(t

Answer 1

Not really.

R(t) = R(P(t)) = 10 * P(t) - P(t)^2 = 10(.25 + .05(t)) - (.25 + .05(t))^2

= 2.5 + .5(t) - 0.0625 - 0.25(t) - 0.0025(t^2)

= 2.4375 + 0.25(t) - 0.0025(t^2).