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22 April, 18:26

Assume that the growth rate of a population of ants is proportional to the size of the population at each instant of time. Suppose 100 ants are present initially and 230 are present after 3 days.

a. Write a differential equation that models the population of the ants.

b. Solve the differential equation with the initial conditions.

c. What is the population of the ants after 14 days?

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  1. 22 April, 18:47
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    (1/A) dA/dt = C where A is the population of ants and C is a constant

    ln (A) = C*t + C1 where C1 is another constant that comes out of integration and t is time in days.

    Plugging in: at t=0, A = 100 so C1 = ln (100) = 4.605

    at t=3, A=230 so ln (230) = 3*C + 4.605 so C = 0.278

    Final equation:

    ln (A) = 0.278t + 4.605

    or:

    A = exp (0.278t + 4.605)

    After 14 days, A = exp (0.278*14 + 4.605) = 4875.2
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