The growth of cancer tumors may be modeled by the Gompertz growth equation. Let M(t) be the mass of the tumor for t ≥ 0. The relevant initial value problem is

where a and K are positive constants and 0 < M₀ < K.

a. Graph the growth rate function R1M2 = -aM ln M/K assuming a = 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 a = 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 equation, what is the meaning of K?

Transcribed Image Text:

M -aM In K’ dM M(0) = Mo- dt