The rate of growth of the profit (in millions of dollars) from a new technology is approximated

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The rate of growth of the profit (in millions of dollars) from a new technology is approximated by P′(t) = te-t2, where t represents time measured in years. The total profit in the third year that the new technology is in operation is $10,000.
(a) Find the total profit function.
(b) What happens to the total amount of profit in the long run?

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