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Math Help - instantaneous rate word problem

  1. #1
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    instantaneous rate word problem

    So I was able to do the first part (hopefully it's right), but I'm having trouble trying to figure out what it's asking in the last parts. Here's my problem:

    A business is prospering in such a way that its total (accumulated) profit after t years is 1000t^2 dollars.

    a) How much did the business make during the third year?
    so, f(3)=1000(3)^2=9000 hopefully its right.

    b) What was its average rate of profit during the first half of the third year, between t=2 and t=2.5?

    c) What was its instantaneous rate of profit at t=2?

    Do I plug in the values for t in part b and c or is there something else invovled? Any help is greatly appreciated!
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  2. #2
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    Quote Originally Posted by ascendancy523 View Post

    b) What was its average rate of profit during the first half of the third year, between t=2 and t=2.5?
    \frac{f(2.5)-f(2)}{2.5-2}


    Quote Originally Posted by ascendancy523 View Post

    c) What was its instantaneous rate of profit at t=2?
    f'(2)
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