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Math Help - please help with this question

  1. #1
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    please help with this question

    A population of a Jellybean is growing exponentially. At the given timet, in years, the population J(t) is given by J(t) = J(0)ekt, where k is a con-stant.
    (a) If the population was 200 in 2007 and 450 in 2012, find k.
    (b) What is the expected population for 2020?
    (c) In what year would you expect the population of Jellybeans to reach one million?
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  2. #2
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    Re: please help with this question

    Quote Originally Posted by mathkid182 View Post
    A population of a Jellybean is growing exponentially. At the given timet, in years, the population J(t) is given by J(t) = J(0)ekt, where k is a con-stant.
    (a) If the population was 200 in 2007 and 450 in 2012, find k.
    (b) What is the expected population for 2020?
    (c) In what year would you expect the population of Jellybeans to reach one million?
    Here are some hints.

    a) J(2007)=200=J_0(e^{2007k}) and J(2012)=450=J_0(e^{2012k}).

    Dividing the two equations gives \frac{200}{450}=e^{2007k-2012k}=e^{5k}. Use this to solve for k. Having solved for k, use either one of the original equations I gave you to solve for J_0

    b) Now that you have values for J_0 and k, simply calculate J(2020)

    c) Solve the equation J(t)=J_0e^{kt}=1,000,000 for t.
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