Let $t$ be time in seconds and let $r(t)$ be the rate, in gallons per second, that water enters a reservoir: $$r(t)=900 - 40 t.$$

(a) Evaluate the expression $\ r(10) =$ .

(b) Which one of the statements below best describes the physical meaning of the value of $r(10)$ ?
A. It is the rate at which the rate of the water entering the reservoir is decreasing when 10 gallons remain in the reservoir.
B. It is the total amount, in gallons, of water in the reservoir after 10 seconds.
C. It is the rate, in gallons per second, at which the water is entering reservoir after 10 seconds.
D. It is the number of seconds until the water is entering to reservoir at a rate of 10 gallons per second.
E. None of the above are correct.

(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. It is the horizontal intercept of the graph of $r(t)$.
 2. It is the vertical intercept of the graph of $r(t)$.

A. It is the number of seconds until the water stops flowing into the reservoir and starts to drain out.
B. It is the initial amount of water, in gallons, in the reservoir.
C. It is the rate, in gallons per second, at which the water is initially entering the reservoir.
D. It is the average rate, in gallons per second, at which water is flowing out of the reservoir.
E. It is the rate at which the rate of water entering the reservoir is decreasing in gallons per second squared.

(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))