Chapter 4.4, Problem 48E

Breast Cancer It has been observed that the following formula accurately models the relationship between the size of a breast tumor and the amount of time that it has been growing.

$V\left(t\right)=1100{\left[1023e^{-0.02415t}+1\right]}^{-4},$

where $t$ is in months and $V\left(t\right)$ is measures in cubic centimeters. Source: Cancer.

a. Find the tumor volume at 240 months.

b. Assuming that the shape of a tumor is spherical, find the radius of the tumor from part a. (Hint: The volume of a sphere is given by the formula $V=\left(4/3\right)\pi r^3.$)

c. If a tumor of size 0.5 ${cm}^3$ is detected, according to the formula, how long has it been growing? What does this imply?

d. Find $\underset{t\to \infty }{\lim }V\left(t\right)$ and interpret this value. Explain whether this makes sense.

e. Calculate the rate of change of tumor volume at 240 months and interpret.