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Math Help - stuck on Derivatives of exponential functions

  1. #1
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    stuck on Derivatives of exponential functions

    The number of XM satellite Radio subscribers, in millions can be approximated by
    f(t)=0.028(3.824)^(t-2001),where t is the year.

    Find the instantaneous rate of change in the number of XM satellite radio subscribers in 2006 years.


    I got f'(2006)=99.3968 ,but I don't know how to give the unit of that answer.
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  2. #2
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    Quote Originally Posted by shannon1111 View Post
    The number of XM satellite Radio subscribers, in millions can be approximated by
    f(t)=0.028(3.824)^(t-2001),where t is the year.

    Find the instantaneous rate of change in the number of XM satellite radio subscribers in 2006 years.


    I got f'(2006)=99.3968 ,but I don't know how to give the unit of that answer.

    The units can be though of as \frac{\Delta f}{\Delta t}

    so in words the change in f over the change in t

    Since f represents the number of subsribers per year and t represents time we get

    The change in the number of subscribers per year.( in Millions)
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    The units can be though of as \frac{\Delta f}{\Delta t}

    so in words the change in f over the change in t
    And so has the units of f divided by the units of t

    Since f represents the number of subsribers per year
    No! f represents the number of subscribers (in a particular year)

    and t represents time we get
    t does not just "represent time", t is measured in years.

    The change in the number of subscribers per year.( in Millions)
    So df/dt is measured in "subscribers per year".
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