Chapter 4.3, Problem 62E

Candy The volume and surface area of a “jawbreaker” for any radius is given by the formulas

$V\left(r\right)=\frac{4}{3}\pi r^3$ and $S\left(r\right)=4\pi r^2$,

respectively. Roger estimates the radius of a jaw breaker while in a person’s mouth to be

$r\left(t\right)=6-\frac{3}{17}t$,

where $r\left(t\right)$ is in millimeters and $t$ is in minutes. Source: Mathematics Teacher.

a. What is the life expectancy of a jawbreaker?

b. Find $dV/dt$ and $dS/dt$ when $t=17$ and interpret your answer.

c. Construct an analogous experiment using some other type of food or verify the results of this experiment.