1) In class, we have talked about an exponential model of population growth K(t) = K(0)e\" where r is constant. Now we want to relax this assumption, and let r vary with time. Derive the equation for K(t) in terms of r(t) (still assuming an exponential growth model). Hint: it might be easiest to write down K(1), then K(2), then K(3),. . ., and substitute