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When a reservoir is created by a dam,50 fish are introduced into the reservoir ,which has an estimated carrying capacity of 8000 fish.

A logistic model of the population is
P(t)= 400,000 / 50 + 795e^-0.5t , where t is measured in years.
How long does it take for the population to reach 5000 fish and 90% of the carrying capacity?

Should I use the derivatives to calculate it?

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4 answers
  1. no use for derivatives here.
    90% of capacity is 7200 fish

    So, just solve for t when P(t) = 5000 or 7200

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  2. Oo..I see..but what to do with e?

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  3. come on, guy. You must have solved exponential problems before, no?

    5000 = 400,000 / (50 + 795e^-0.5t)
    50 + 795e^-.5t = 80
    795e^-.5t = 30
    e^-.5t = 30/795
    -.5t = log(30/795)
    t = -2log(30/795) = 6.55

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  4. Sorry,totally forgot about that..
    Thanks^^

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