Chapter 14.6, Problem 43E

Exercises 41–44 require the use of technology.

Growth of Tumors The growth of tumors in animals can be modeled by the Gompertz equation:

$\frac{dy}{dt}=-ay\ln \left(\frac{y}{b}\right),$ where y is the size of a tumor, t is time, and a and b are constants that depend on the type of tumor and the units of measurement.

a. Solve for y as a function of t.

b. If $a=1,b=10\text{ and }y\left(0\right)=5$ cubiccentimeters (with t measured in days), find the specific solution and graph it.