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25 August, 22:31

The number of bacteria in a certain population increases according to an exponential growth model, with a growth rate of 3.5% per hour.

How many hours does it take for the size of the sample to double?

Do not round any intermediate computations, and round your answer to the nearest hundredth.

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  1. 25 August, 23:48
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    Generic exponential growth model: y = Ao[1+r]^t

    In this case: r = 3.5% = 0.035

    y = 2Ao ... [the double of the initial value]

    Then: 2Ao = Ao (1 + 0.035) ^t

    (1.035) ^t = 2

    Take logarithm to both sides

    t ln (1.035) = ln (2)

    t = ln (2) / ln (1.035) = 0.693 / 0.0344 = 20.15

    Answer: 20.15 hours.
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