Calculus
posted by Sarah on .
The rate of growth of the profit is approximated by P'(x)=xe^(x^2) where x represents time measured in years. The total profit in the third year that the new technology is in operation is $10,000.
1.Find the total profit function
2. what happens to the total amount of profit in the long run?

dp/dt = t e^t^2
if p = c  .5e^t^2
p' = t e^t^2 =
when t = 3
10,000 = c  .5e^9
c = 10,000 + .5 e^9
c = 10,000 + .0000617
so
p = 10,000  .5/ e^(t^2) essentially
It becomes 10,000 as t> oo