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Math Help - Exponential Word Problem

  1. #1
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    Exponential Word Problem

    I would love to show some effort here, but I honestly have no idea were to start, any help would be greatly appreciated.

    Initially there are two snow goons. We need to estimate the amount of time it takes each snow goon to make 100 new snow goons. Let t = the number of days since the first two snow goons were made. Let N(t) = the number of snow goons on day t.
    Estimate: On day t = 3 we estimate that there will be 100 snows goons.


    1. On day t = 0 there are N = ____ snow goons. This is the initial amount.
    The blank is 2 I'm assuming.

    2. Find a function of the form N(t) = (C)e^kt that gives N(t), the number of snow goons that exist t days after the first two are built.

    Wouldn't the number of snow goons just double everytime? I think the wording is throwing me off or I am over thinking this. Thanks.
    Last edited by pmahoney1337; November 27th 2011 at 05:58 PM.
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  2. #2
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    Re: Exponential Word Problem

    Quote Originally Posted by pmahoney1337 View Post
    I would love to show some effort here, but I honestly have no idea were to start, any help would be greatly appreciated.

    Initially there are two snow goons. We need to estimate the amount of time it takes each snow goon to make 100 new snow goons. Let t = the number of days since the first two snow goons were made. Let N(t) = the number of snow goons on day t.

    Find a function of the form N(t) = (C)e^kt that gives N(t), the number of snow goons that exist t days after the first two are built.

    Wouldn't the number of snow goons just double everytime? I think the wording is throwing me off or I am over thinking this. Thanks.
    N(0) = 2

    N(t) = 2e^{kt}

    want to solve for t when N(t) = 102

    102 = 2e^{kt}

    you need another bit of info about the population after t = 0 to determine the growth constant k , then you'll be able to find t
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  3. #3
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    Re: Exponential Word Problem

    Hmmm, that's weird because I gave you all the information I'm given.

    There is a part before that question that asks me to make an estimate of how many snow goons there would be after t amount of days, but I don't see how an estimate would help here.
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    Re: Exponential Word Problem

    I edited the original problem so maybe it is solvable now.
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  5. #5
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    Re: Exponential Word Problem

    need to estimate the amount of time it takes each snow goon to make 100 new snow goons.
    edit the equation ...

    202 = 2e^{kt}

    Estimate: On day t = 3 we estimate that there will be 100 snows goons.
    100 \approx 2e^{k \cdot 3}

    solve an estimate for k, then use the result to estimate t in the first equation.
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  6. #6
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    Re: Exponential Word Problem

    EDIT: Never mind I get it. Thanks, I'll keep posting if I have questions.
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  7. #7
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    Re: Exponential Word Problem

    Ok I did what you said and got 202 = (2)e^1.3(3.55). Not sure if that is right, but even if it is I need the function to give me N(t) right?

    So would the answer be N(t) = (2)e^(1.3)t?
    Last edited by pmahoney1337; November 27th 2011 at 06:37 PM.
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