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The Gompertz growth equation is often used to model the growth of tumors. let M(t) be...

The Gompertz growth equation is often used to model the growth of tumors. let M(t) be the mass of a tumor at time t>0. the relevant initial value problem is;

dM/dt=-rMln(M/K),M(0)=m*subscript 0, where r and k are positive constants and 0<m*subscript0<K. solve the initial value problem and graph the solution for r=1 and k=4, and M*subscript0=1. Describe the growth pattern of the tumor. Is the growth unbounded? if not, what is the limiting size of the tumor?

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