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Math Help - Exponential Bacteria

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    Exponential Bacteria

    Suppose that a bacterial culture is growing exponentially and the culture doubles every 12 hours. Obtain a formula for the number Pn of square millimeters of culture expected in n hours given that the culture measured 5 square millimeters when first observed.
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    Quote Originally Posted by WartonMorton View Post
    Suppose that a bacterial culture is growing exponentially and the culture doubles every 12 hours. Obtain a formula for the number Pn of square millimeters of culture expected in n hours given that the culture measured 5 square millimeters when first observed.
    If we assume that when the population doubles the area it occupies is also doubled we can reason as follows: after n hours, there have been n/12 doublings, therefore we get an area of P_n = 2^{n/12}\cdot 5\mathrm{mm}^2=\left(2^{1/12}\right)^n\cdot 5\mathrm{mm}^2\approx 1.0595^n\cdot 5\mathrm{mm}^2.
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