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Math Help - Exponential function help

  1. #1
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    Exponential function help

    U.S.Department estimatedthat there were 54 million Internet users in the country in 1999 and 85 millionusers in 2002.
    a)
    t(years after 1995 4 17
    internet users (millions) ? ?

    b)Use the information on the table to obtain an exponential function that models then umber of Internet users as a function of the time, U(t)=U0e^kt
    c)rate of increase of the number of internet users in the US?
    d) number of Internet users in the US in 2013 according to your model?
    e)
    If the population of the U.S. is approximately 314 million, for how long is this model likely to remain accurate?
    new to this having problems trying to solve it
    Last edited by John108; December 10th 2013 at 01:57 PM.
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  2. #2
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    Re: Exponential function help

    part (a) isn't understandable as posted. Could you repost this and fix the formatting?

    Have you tried any of this? Do you have any work so far you can post?
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  3. #3
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    Re: Exponential function help

    okay fixed it. im new to this and having issues trying to approach and solve this problem
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  4. #4
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    Re: Exponential function help

    the data on #internet users came through as ?'s

    I'm going to guess you want to model the data as a a scaled exponential function

    N = A eb(t-t0)

    where
    N = #internet users
    t = current year
    t0 = some reference year. This is optional but useful. You specify this.

    A and b are parameters to be solved for.

    If you take the log of both sides you get

    ln(N) = ln(A) + b(t-t0)

    This is now just a line in t with slope b and value ln(A) at t=t0.

    You can do a linear regression using t0 and data samples of t and ln(N) to get least square estimates of ln(A) and b.

    then plug those parameter estimates into your exponential formula for N to get the estimate of N given some year t.
    Last edited by romsek; December 10th 2013 at 02:16 PM.
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    Re: Exponential function help

    i need to figure out what would go there
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  6. #6
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    Re: Exponential function help

    oh duh.. the data is in the word problem. Sorry.

    basically you'd do what I just went through with
    t0 = 1995
    t = {1999, 2002}
    N = {54, 85} in millions

    now use the parameters you solved for in the exponential model to forecast for t = {1995+5, and 1995+17}
    Thanks from John108
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  7. #7
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    Re: Exponential function help

    what i did for B) was u(t)=U0e^kt
    y=ab^x
    y=(29.5)(1.163)^x

    k=ln3
    k=ln(1.163)^x
    k=0.151
    increase at 15.1%
    U(t)=29.5e^(0.151)(t)


    for D) 2013 t=18
    U(t)=29.5e^0.151^(18)
    U(t)=446.9 million

    for E) (314/29.5)= 29.5e^0.151(t) /29.5
    10.64=e^0.151(t)
    ln(10.64)=ln(0.151(t)e)
    ln(10.64)=(0.151)(t)
    ln(10.64)/0.151=t
    t=15.7 years


    can you check it out
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  8. #8
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    Re: Exponential function help

    this isn't very clear.

    this is what I got

    Exponential function help-clipboard01.jpg

    first normalize the years by subtracting 1995
    then take the Log of the users
    rearrange the data so it's in the form {normalized year, Log(users)}

    Let Mathematica find the best linear fit

    Pull the coefficients out and label them as I said in my earlier post.
    Convert lnA to A by taking it's exponential

    Write the function that's your exponential model as I explained.
    Use this function to estimates the #users in 1999, and 2012

    Double check estimate for years we have data on.
    Last edited by romsek; December 10th 2013 at 03:46 PM.
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