Let $t$ be time in seconds and let $r(t)$ be the rate, in gallons per second, that water enters a reservoir: $$r(t)=700 - 30 t.$$

(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. How many seconds until the water is entering to reservoir at a rate of 5 gallons per second.
B. The rate, in gallons per second, at which the water is entering reservoir after 5 seconds.
C. The rate at which the rate of the water entering the reservoir is decreasing when 5 gallons remain in the reservoir.
D. The total amount, in gallons, of water in the reservoir after 5 seconds.
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.

 1. The slope of the graph of $r(t)$.
 2. The vertical intercept of the graph of $r(t)$.

A. The initial amount of water, in gallons, in the reservoir.
B. How many seconds it takes until there is no longer any water in the reservoir.
C. The rate at which the rate of water entering the reservoir is decreasing in gallons per second squared.
D. The average rate, in gallons per second, at which water is flowing out of the reservoir.
E. The rate, in gallons per second, at which the water is initially entering the reservoir.

(d) For $0 \leq t \leq 40$, when does the reservoir have the most water?
When $t =$ sec.

(e) For $0 \leq t \leq 40$, when does the reservoir have the least water?
When $t =$ sec.

(f) If the domain of $r(t)$ is $0 \leq t \leq 40$, what is the range of $r(t)$?
range = (enter your answer in interval notation, or an inequality in $r$: help (inequalities))