(Growth of Cells) Suppose that after t hrs, there are p (t) cells present in a culture, where P(t) = 5000e*^2t

a) How many cells were present initially?
b) Give a differential equation satisfied by P(t)
c) When will the population double?
d) When will 20,000 cells be present?

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  1. a. "initially" means time = 0
    P(0) = 5000e^2(0) = 5000e^0 = 5000

    b. P(t) = 5000*e^(2t)

    [d/du]e^u = e^u du

    Therefore, P'(t) = 5000*2e^(2t)
    P'(t) = 10000e^(2t)

    c. Set e^(2t) = 2.
    2t = ln2
    t = (ln2)/2

    The population will double every (ln2)/2 hours.

    d. set P = 20000 and solve for t.

    20000 = 5000e^(2t)
    4 = e^(2t)
    ln4 = 2t
    2ln2 = 2t
    ln2 = t

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