$(4)$ A gas station sits at the intersection of a north$-$south road and an east$-$west road. A police car is traveling toward the gas station from the east, chasing a stolen truck which is traveling north away from the gas station. The speed of the police car is $80$ mph at the moment it is $5$ miles from the gas station. At the same time, the truck is $12$ miles from the gas station going $60$ mph $.$ At this moment, is the straight$-$line distance between them increasing or decreasing? At what rate?

$(5)$ The concentration of antibiotic in the bloodstream $t$ hours after being injected is modeled by the function $C(t)=\frac{2t}{t^2+4},$ where $C$ is measured in milligrams per liter of blood.

$($a$)$ Use the Intermediate Value Theorem to show that, at some time in the first $2$ hours, the concentration of the antibiotic is exactly $\frac{1}{4}$ milligrams per liter of blood.

$($b$)$ What is the long term behavior of the concentration of the antibiotic?