Question
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?
1.Find the total profit function
2. what happens to the total amount of profit in the long run?
Answers
Damon
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
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