Question

a tank is filling up at a constant rate. the number of gallons of water in the tank ,y, after it has been filling up for x minutes is given in the table below.

time (minutes)	water (gal)
20	45.9
30	59.2
40	72.5

what is the rate of change of the represented in the table?
13.3 gallons per minutes
-1.33 gallons per minute
0.33 gallons per minute
1.33 gallons per minutes

Explanation:

Step1: Recall rate - of - change formula

The rate of change (slope) formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Select two points from the table

Let's take $(x_1,y_1)=(10,32.6)$ and $(x_2,y_2)=(20,45.9)$.

Step3: Calculate the rate of change

$m=\frac{45.9 - 32.6}{20 - 10}=\frac{13.3}{10}=1.33$.

Answer:

1.33 gallons per minute