Pre calc

The general function P(t)= 640ekt is used to model a dying bird population, where Po = 640 is the initial population and t is time measured in days. Suppose the bird population was reduced to one quarter of its initial size after 9 days. How long will it take before there are only 40 birds left in the population? Simplify your answer as much as possible.

PLease help and show all work Thank you!

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  1. I am positive that you meant:
    P(t) = 640 e^(kt)
    given: when t = 9, P(t) = 160
    640 e^(9k) = 160
    e^(9k) = .25
    9k = ln .25
    k = ln.25/9 = -.154033

    640 e^( -.154033 t) = 40
    e^(-.154033 t) = .0625
    -.154033 t = ln .0625
    t = ln .0625/-.154033 = 18 days

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  2. It took 9 days to shrink to 1/4 its size.

    40/640 = 1/16 = 1/4 * 1/4

    So, it will take another 9 days to do that again.

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