N(t) satisfies the differential equation  $\frac{dN}{dt}=ke^{at}N$dNdt =ke^atN , a and t are constants and t is the time. Use serperation of variables and the intial  condition N(0)= N(knot) to show that N(t)= $N\left(knot\right)e^{\frac{k\left(e^{at}-1\right)}{a}}$N(knot)e^k(eat−1)a