Chapter 4.3, Problem 43E

Size of Tumor In a study, a cancerous tumor was found to have a volume of

$f(t)=1.825{(1-1.6e^{-0.4196t})}^3$

Millimetres after $t$ weeks, with $t>1$. (Source: Growth, Development and Aging.)

a. Sketch the graph of $f(t)$ and $f\text{'}(t)$ for $1\le t\le 15$.What do you notice about the tumor’s volume ?

b. How large is the tumor have a volume after $5$ weeks ?

c. When will the tumor have a volume of $5\text{mililiters}$?

d. How fast is the tumor growing after $5$ weeks ?

e. When is the tumor growing at the fastest rate ?

f. What is the fastest rate of growth of the tumor ?