To describe the rate of change for the relationship between the time since Tracy filled her gas tank and the amount of gas left in the tank, we need to consider the context of driving.
Let's assume that Tracy drives a vehicle that consumes a certain number of gallons of gas per hour. For example, if Tracy's car consumes 3 gallons of gas per hour, the relationship can be expressed as follows:
- Let \( t \) be the time in hours since filling the gas tank.
- Let \( g \) be the amount of gas left in gallons.
If she starts with a full tank of gas (let's say 30 gallons for this example), the amount of gas left after \( t \) hours would be:
\[ g = 30 - 3t \]
In this case, the rate of change is the amount of gas consumed per hour.
Thus:
The rate of change for this relationship is \(-3\) gallons of gas per hour.
This means the amount of gas left decreases by 3 gallons for every hour that Tracy drives. The negative sign indicates that the amount of gas is decreasing over time. If you know Tracy's actual vehicle's fuel consumption rate, you can replace 3 with that specific rate to accurately describe the situation.
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