Struggling with this differential equation problem

Question

Suppose that a population grows according to the unlimited growth model described by the differential equation dy/dt=0.2y and we are given the initial condition y(0)=600. Find the size of the population at time t=5

Answer 1

To solve this question, you need to find y(t), which actually isn't that difficult.

The biggest challenge is that you need to integrate dy/dt, which might seem challenging, but not if you remember to separate first, and integrate second.

$\frac{dy}{dt} = 0.2y$ is the same as $\frac{1}{.2y} dy = dt$.

If we integrate both sides, we get

$ln(.2y) = t + C$, for some constant $C$.

Remember that y is really the function y(t). So, if we solve for y in the above equation, we actually get just what we want!

Can you take it from here? (Hint: Remember that to get rid of the log on the left, you can exponentiate the entire equation! And then use the initial condition to find C)