$(1$ point$)$ Let $t$ be time in seconds and let $r(t)$ be the rate, in gallons per second, that water enters a reservoir:

$r(t)=800-40t$

$($a$)$ Evaluate the expression $r(5)=$

$($b$)$ Which one of the statements below best describes the physical meaning of the value of $r(5)?$

A$.$ The total amount, in gallons, of water in the reservoir after $5$ seconds.

B$.$ The rate at which the rate of the water entering the reservoir is decreasing when $5$ gallons remain in the reservoir.

C$.$ The rate, in gallons per second, at which the water is entering reservoir after $5$ seconds.

D$.$ How many seconds until the water is entering to reservoir at a rate of $5$ gallons per second.

E$.$ None of the above

$($c$)$ For each of the mathematical expressions below, match one of the statements $A-E$ below which best explains its meaning in practical terms.

The slope of the graph of $r(t).$

The horizontal intercept of the graph of $r(t).$

A$.$ The rate, in gallons per second, at which the water is initially entering the reservoir.

B$.$ After how many seconds the water stops flowing into the reservoir and starts to drain out.

C$.$ How many seconds it takes until there is no longer any water in the reservoir.

D$.$ The rate at which the rate of water entering the reservoir is decreasing in gallons per second squared.

E$.$ The initial amount of water, in gallons, in the reservoir.

$($d$)$ For $0q,$

When $t=$ sec$.$

$($e$)$ For $0t30,$ when does the reservoir have the least water?

When $t=$ sec$.$

$($f$)$ If the dnmain of $r(t)$ is $0t30,$ what is the range of $r(t)?$ range $=($enter your answer in interval notation, or an inequality in $r$ : help $($inequalities$))$