A petri dish has 10, 000 bacteria in it. After 4 hours the bacteria’s population increased to 20,000. If the number of colonies grows expone

Question

A petri dish has 10, 000 bacteria in it. After 4 hours the bacteria’s population increased to 20,000. If the number of colonies grows exponentially, write a formula for the number of bacteria in the dish at any time t, where t is in hours

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Phúc Điền 5 years 2021-08-18T04:21:26+00:00 1 Answers 65 views 0

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  1. Maris
    0
    2021-08-18T04:23:19+00:00
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    Answer:

    P(t) = 10000e^{0.1733t}

    Step-by-step explanation:

    The population of bacteria grows exponentially, which means that it can be represented by a function in the following format:

    P(t) = P(0)e^{rt}

    In which P(0) is the initial population and r is the growth rate.

    A petri dish has 10, 000 bacteria in it.

    This means that P(0) = 10000. So

    P(t) = 10000e^{rt}

    After 4 hours the bacteria’s population increased to 20,000.

    This means that P(4) = 20000, and we use this to find the growth rate. So

    P(t) = 10000e^{rt}

    20000 = 10000e^{4r}

    e^{4r} = \frac{20000}{10000}

    e^{4r} = 2

    \ln{e^{4r}} = \ln{2}

    4r = \ln{2}

    r = \frac{\ln{2}}{4}

    r = 0.1733

    So, the formula is given by:

    P(t) = 10000e^{0.1733t}

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