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 initial amount of water in the tank?
1.33 gallons
10 gallons
19.3 gallons
32.6 gallons

Explanation:

Step1: Find the rate of filling

The rate of change (slope) $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(10,32.8)$ and $(20,45.9)$. Then $m=\frac{45.9 - 32.8}{20 - 10}=\frac{13.1}{10}=1.31$.

Step2: Use the point - slope form of a line

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(10,32.8)$ and $m = 1.31$, we have $y-32.8=1.31(x - 10)$.

Step3: Find the initial amount (when $x = 0$)

When $x = 0$, we substitute into the equation $y-32.8=1.31(0 - 10)$. So $y-32.8=1.31\times(- 10)=-13.1$. Then $y=32.8-13.1 = 19.3$.

Answer:

19.3 gallons