Matlab

3 points Problem 3 Population growth problems often give rise to rate equations that are first-order. For example, the equation dN dt might describe how the nmumber of individuals in a population, N, varies with time. Here the first term aN corresponds to the birth of new members, while the second term -bN2 corresponds to deaths. The deatlh term is proportional to N2 to allow for the fact that food will become harder to find when the population N becomes large. Plot the solution of the differential equation with b = 0 using the Euler method, and compare your numerical result with the exact solution. Then solve the differential equation with nonzero values b. Interesting values of a and b depend on the initial population N. For small N(0), a = 10 and b = 3 is a good choice, while for N(0) =00 a good choice is a = 10 and b-0.01. Graphically represent your results. 4 points