Posted by Sarah on Sunday, April 11, 2010 at 2:56pm.
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?

Calculus  Reiny, Sunday, April 11, 2010 at 3:43pm
If P'(x)=xe^(x^2) , then
P(x) = (1/2) e^(x^2) + c
when t= 3 , P(3) = 10000
10000= (1/2)e^(9) + c
10000 = .00006 + c
c = 10000.0000617
1. P(x) = (1/2) e^(x^2) + 10000.0000617
2. "in the long run" implies x >∞
which means (1/2) e^(x^2) > 0
so P(∞) = 10000.0000617
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