If population is changed either by immigration or emigration, the exponential growth model discussed in Section 1 is modified to

where y is the population at time t and f(t) is some (other) function of t that describes the net effect of the emigration/ immigration. Assume k = 0.02 and y(0) = 10,000. Solve this differential equation for y, given the following functions f(t).

ƒ(t) = e^-t

dy dt = ky + f(t),