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26 July, 21:27

the population P of a bacteria culture is modeled by P=4300e^kt, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double?

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  1. 26 July, 21:49
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    93 h

    Step-by-step explanation:

    P = 4300eᵏᵗ

    1. Calculate the value of k

    lnP = ln4300 + kt

    ln5800 = ln4300 + k (40 h)

    8.666 = 8.366 + 40k h

    8.666 - 8.366 = 40k h

    0.299 = 40 k h

    k = 0.299/40 h = 7.481 * 10⁻³ h⁻¹

    2. Calculate the time for the population to double

    2 * 4300 = 4300eᵏᵗ

    2 = eᵏᵗ

    ln2 = kt

    t = ln2/k = ln2 / (7.481 * 10⁻³ h⁻¹) = 93 h

    It takes 93 h for the population to double.
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