Chapter 3.3, Problem 36E

Mass of Bighorn Yearlings The body mass of yearling bighorn sheep on Ram Mountain in Alberta, Canada, can be estimated by

$M\left(t\right)=27.5+0.3t-0.001t^2$

Where $M\left(t\right)$ is measured in kilograms and $t$ is days since May $25$.

Source: Canadian Journal of zoology.

a. Find the average rate of change of the mass of bighorn yearling between $105$ and $115$ days past May $25$.

b. Find the instantaneous rate of change of the mass for a bighorn yearling sheep whose age is $105$ days past May $25$.

c. Graph the function $M\left(t\right)$ on $[5,125]$ by $[25,65]$.

d. Does the behavior of the function past $125$ days accurately model the mass of the sheep? Why or why not?

e.

f.

g.