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Math Help - The number of Americans...

  1. #1
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    Question The number of Americans...

    The number of Americans,in thousands who are expected to be over 100years old is approximated by n(t)=0.4018t^2+2.039t+50.71,where t is the year with t=0 corresponding to 1994.Determine the year that the number of Americans expected to be over 100 years old was increasing at a rate of 6000 people per year.
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by mathcalculushelp View Post
    The number of Americans,in thousands who are expected to be over 100years old is approximated by n(t)=0.4018t^2+2.039t+50.71,where t is the year with t=0 corresponding to 1994.Determine the year that the number of Americans expected to be over 100 years old was increasing at a rate of 6000 people per year.
    Take the derivative, set it equal to 6 (because the equation is per thousand people), and solve for t. You should get t\approx4.93, which implies that the year was around 1999.
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  3. #3
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    find n'(t) = 6 and add 1994 to your answer.

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