After a new firm starts in business, it finds that its rate of profit (in hundreds of dollars) after t years of operation is given by $P'(t) = 3t^2 + 2t + 10$. Find the profit in year 6 of the operation. A. $30,000 B. $20,000 C. $25,600 D. $11,200
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We want to find the profit in year 6. This means we need to find the total profit from year 0 to year 6. To do this, we need to integrate the rate of profit function with respect to time from 0 to 6. $$P(t) = \int P'(t) dt = \int (3t^2 + 2t + 10) dt$$ Show more…
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