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16 March, 00:30

Researchers recorded that a certain bacteria population declined from 100,000 to 100 in 24 hours. At this rate of decay, how many bacteria were there 8 hours into the experiment?

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  1. 16 March, 03:29
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    9990bacterias

    Step-by-step explanation:

    Using the formula for finding rate of decay.

    N (t) = Noe^-kt

    No is the initial population

    N (t) is the population during time, t

    If bacteria population declined from 100,000 to 100 in 24 hours

    No = 100,000, N (t) = 100, t = 24

    Substituting to get the constant k

    100 = 100000e^-24k

    0.001 = e^-24k

    Taking ln of both sides

    ln0.001 = lne^-24k

    -6.91 = - 24k

    k = 6.91/24

    k = 0.288.

    To know the number of bacteria there after 8hours,

    N (8) = 100,000e^-0.288 (8)

    N (8) = 100,000e^-2.304

    N (8) = 100,000*0.0999

    N (8) = 9,990bacterias
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