Message Board Assignment (Ch7) 7) Consider the following function f(N) with parameters a and b both strictly greater than 0. vy = (ZINIRGIND N #0 a) Use L'Hopital's Rule to show that f(N) is continuous at N=0. b) Find and classify all equilibrium values of the first order autonomous differential equation given by ZT = f(N) as either stable, unstable, or semi-stable. Answers may be in terms of a and b. ) Draw out the Phase Diagram of the system. Let t be the x-axis and N(t) be the y-axis. d) When we restrict the values of N to be strictly greater than 0, we get the following: a_ N In(bN ar n(bN) This differential equation is known as Gompertz Law, and it's used to model the growth of cancerous tumors, where N(t) is proportional to the number of cells in the tumor and a,b>0 are parameters. Find the general solution N(t) for Gompertz Law. e) If weleta = 0.09 and b = 0.01, then N(t) represents a particular tumot's size N as a percentage of its maximum potential size, where time t is measured in days. If initially (time t = 0) the tumor is at 10% its maximum size (N = 10), how many days will it be before the tumor reaches 90% of its maximum size (N = 90)