To determine the rate of change for the relationship between time (in minutes) and the amount of water in the bathtub (in gallons), you need to analyze how the water level changes over the given time intervals. The rate of change in this context is essentially how much the water level decreases per minute.
Looking at the time and water levels:
- At 7 minutes, the water level is 38.5 gallons.
- At 8 minutes, the water level is 36.25 gallons.
Calculate the change in water level:
[tex]\[
\text{Change in water level} = 36.25 \text{ gallons} - 38.5 \text{ gallons} = -2.25 \text{ gallons}
\][/tex]
Calculate the corresponding change in time:
[tex]\[
\text{Change in time} = 8 \text{ min} - 7 \text{ min} = 1 \text{ min}
\][/tex]
The rate of change is given by the ratio of the change in water level to the change in time:
[tex]\[
\text{Rate of change} = \frac{\text{Change in water level}}{\text{Change in time}} = \frac{-2.25 \text{ gallons}}{1 \text{ min}} = -2.25 \text{ gal/min}
\][/tex]
Thus, the rate of change for the relationship is [tex]\(-2.25\)[/tex] gallons per minute. This negative rate indicates that the water level in the bathtub is decreasing by 2.25 gallons each minute.
