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13 November, 09:33

The rate of growth of a certain cell culture is proportional to its size. In 10 hours a population of 1 million cells grew to 99 million. How large will the cell culture be after 25 hours

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  1. 13 November, 09:48
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    98 billion

    Explanation:

    1. Expression for rate of growth

    Let Po = the original population

    and P = the population at time t. Then

    dP/dt = kP

    dP/P = kdt

    lnP = kt + C

    At t = 0, lnPo = C

    lnP = kt + lnPo

    ln (P/Po) = kt

    2. Value of k

    ln (99 million/1 million) = k (10)

    ln99 = 10k

    k = ln99/10 = 4.595/10 = 0.4595/h

    ln (P/Po) = 0.4595t

    3. Population after 25 h

    ln (P/Po) = 0.4595 * 25 = 11.49

    P/Po = e^ (11.49) = 97 519

    P = 97519No = 97 519 * 1 * 10^6 = 9.8 * 10^10 = 98 * 10^9

    P = 98 billion.

    In 25 h the population of the cell culture will be 98 billion.
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