It is projected that t months from now, the average price per unit for goods in a certain sector of the economy will be P dollars, where

a. At what rate will the price per unit be increasing with respect to time 5 months from now?

b. At what rate will the rate of price increase be changing with respect to time 5 months from now?

c. Use calculus to estimate the change in the rate of price increase during the first half of the sixth month.

d. Compute the actual change in the rate of price increase during the first half of the sixth month.

P(t) = 1 + 7t + 200t + 300