To find the rate of change in the number of gallons in the pool between the points (1, 160) and (3, 80), we can use the formula for the rate of change (slope) between two points:
\[ \text{Rate of Change} = \frac{y2 - y1}{x2 - x1} \]
Here, \((x1, y1) = (1, 160)\) and \((x2, y2) = (3, 80)\).
Now, plug in the values:
\[ \text{Rate of Change} = \frac{80 - 160}{3 - 1} \]
Calculate the numerator:
\[ 80 - 160 = -80 \]
Calculate the denominator:
\[ 3 - 1 = 2 \]
Now, substitute these values back into the formula:
\[ \text{Rate of Change} = \frac{-80}{2} = -40 \]
Thus, the rate of change in the number of gallons in the pool after each hour has passed is \(-40 , \text{gal./hr.}\)
The correct response is:
−40 gal./hr.