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Math Help - Please check answer for percentage rate of change function

  1. #1
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    Please check answer for percentage rate of change function

    The question is to determine the percentage rate of change of the function at t=1 and t=5 for:

    f(t)=e^{0.3t^2}

    I calculated the derivative to be:
    f'(t)=e^{0.3t^2}0.6t

    So is the answer to t=1, an increase of 60%?

    And for t=5, 750%?
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  2. #2
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    Quote Originally Posted by Kataangel View Post
    The question is to determine the percentage rate of change of the function at t=1 and t=5 for:

    f(t)=e^{0.3t^2}

    I calculated the derivative to be:
    f'(t)=e^{0.3t^2}0.6t

    So is the answer to t=1, an increase of 60%?

    And for t=5, 750%?
    For t= 1, yes, for t= 5, no.

    The rate of increase is, as you say, the derivative, f'. The percentage rate of increase is that, divided by f: f'/f= [tex]\frac{e^{0.3t^2}0.6t}{e^{0.3t^2}}= 0.6t. For t= 1, that is .6(1)= .6 or 60%. For t= 5, that is .6(5)= 3.0 or 300%.
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