Calculus

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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 -

    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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