$17\mathrm{.}4$ At a time $t$ seconds after a ball is thrown up in to the air, it is at a height of

$f(t)=-4\mathrm{.}9t^2+16t+1$ meters.

$($a$)$ What is the average velocity of the ball during the first second? Give units.

$($b$)$ Find the instantaneous velocity of the ball at $t=1.$ Give units.

$17\mathrm{.}5$ In $[71],$ Steury and Murray model the cyclic trends of a hare population using

$H(t)\frac{?}{b}=ar(b)+\frac{m}{2}cos(\frac{2t}{10})$

where $H(t)$ is the density of the hare population measured in hares per hectare at year $t\frac{,}{b}ar(b)$ is the average hare density, and $m$ is the difference between high and low hare densities. A particular population of hares has an average density of $1\mathrm{.}06$ hares$/$hectare$,$ with a minimum density of $0\mathrm{.}31$ hares$/$hectare and a maximum density of $1\mathrm{.}81$ hares$/$hectare$.$

$($a$)$ How does this population vary with time? Using Matlab, graph $H(t)$ for $5$ years.

$($b$)$ Use the graph to determine at what times the population reaches a maximum value. A minimum value. Does the population density maxima and minima