Question

A bathtub is filled with 40 gallons of water. The water starts draining out of the tub at a rate of 8 gallons per minute. Choose the sketch of a graph that shows the relationship between the number of minutes since the tub started draining and the number of gallons of water in the tub.
A. (0, 5) and (0, 40) in a straight line.
B. (0, 5) and (0, 40) in a curvy line.
C. (0, 8), and (0, 40) in a straight line.
D. (0, 5), and (0, 40) in a curvy line.

Answer 1

A.

At t = 0, the tub has 40 gallons. The amount is linear in time with rate −8 gal/min: V(t) = 40 − 8t. V(t) reaches 0 when 40 − 8t = 0 ⇒ t = 5, so the line goes through (0,40) and (5,0). The graph is a straight line decreasing between those points.