The rate of growth dP/ dt of a population of bacteria is proportional to the square root of t with a constant coefficient of 9, where P is the population size and t is the time in days (0¡Üt¡Ü10). The initial size of the population is 700. Approximate the population after 7 days. Round the answer to the nearest integer.

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  1. dP/dt = 9√t
    P(t) = 6t^(3/2)+c
    P(0) = 700, so c=700 and thus

    P(t) = 6t^(3/2)+700

    as you can see, this function models some slow growth. You sure dP/dt is not proportional to P?

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