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Math Help - Integration (population growth)

  1. #1
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    Integration (population growth)

    A population of bacteria is changing at a rate of

    dP/dt = 3000/(1+0.25t)

    where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t, and find the population when t=3 days.
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  2. #2
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    Quote Originally Posted by saiyanmx89 View Post
    A population of bacteria is changing at a rate of

    dP/dt = 3000/(1+0.25t)

    where t is the time in days. The initial population (when t=0) is 1000. Write an equation that gives the population at any time t, and find the population when t=3 days.
     \frac{dP}{dt} = \frac{3000}{1+0.5t}

     dP = 3000  \times \frac{dt}{1+0.5t}

     \int {dP} =  3000 \int \frac{dt}{1+0.5t}

     P = 3000 \int  \ln{|1+0.5t|} + C

    If you plug in t = 0, P = 1000, you can find C.
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