Tumor growth The Gompertz growth equation is often used to

Chapter , Problem 49

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Tumor growth The Gompertz growth equation is often used to model the growth of tumors. Let M1t2 be the mass of a tumor at time t 0. The relevant initial value problem is dM dt = -rM ln a M K b, M102 = M0, where r and K are positive constants and 0 6 M0 6 K. a. Graph the growth rate function R1M2 = -rM ln a M K b (which equals M_1t2) assuming r = 1 and K = 4. For what values of M is the growth rate positive? For what value of M is the growth rate a maximum? b. Solve the initial value problem and graph the solution for r = 1, K = 4, and M0 = 1. Describe the growth pattern of the tumor. Is the growth unbounded? If not, what is the limiting size of the tumor? c. In the general solution, what is the meaning of K?