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Math Help - Exponential Growth

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    Exponential Growth

    Suppose that a colony of bacteria is growing exponentially. Let M represent the mass in grams of the colony after t hours. If M satisfies M'(t)=.12M(t) and M(6)=37, find M(t).
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    Quote Originally Posted by Velvet Love View Post
    Suppose that a colony of bacteria is growing exponentially. Let M represent the mass in grams of the colony after t hours. If M satisfies M'(t)=.12M(t) and M(6)=37, find M(t).
    the derivative models the law of natural exponential growth ...

    y' = ky

    which has the general solution ...

    y = y_0e^{kt}

    you have k = .12 and M(6) = 37 ... solve for M_0
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    Quote Originally Posted by Velvet Love View Post
    Suppose that a colony of bacteria is growing exponentially. Let M represent the mass in grams of the colony after t hours. If M satisfies M'(t)=.12M(t) and M(6)=37, find M(t).
    If the colony is growing exponentially then the mass at time t satisfies:

    M(t)=M(0)e^{kt}

    where M(0) is the mass at time t=0 and k is a constant.

    Now use the given information to find M(0) and k

    CB
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    When you say M sub 0, do you mean y sub 0?
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    Quote Originally Posted by skeeter View Post
    the derivative models the law of natural exponential growth ...

    y' = ky

    which has the general solution ...

    y = y_0e^{kt}

    you have k = .12 and M(6) = 37 ... solve for M_0

    Alright. I solved for M sub 0, and I got ln(37)/.72
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    Quote Originally Posted by Velvet Love View Post
    When you say M sub 0, do you mean y sub 0?
    Please quote the post you are refering to, that way there will be no confusion.

    CB
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    Quote Originally Posted by Velvet Love View Post
    When you say M sub 0, do you mean y sub 0?
    I expect that you are able to take the general model (where y indicates the dependent variable), and change the dependent variable to suit your specific problem, like so ...

    M = M_0e^{0.12t}
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