To solve the problem, let's follow the steps:
1. Understand the rate of change:
The rate at which the water drains from the bathtub is given as [tex]\(-3.75\)[/tex] gallons per hour. This negative value indicates that the water level is decreasing.
2. Determine the length of time:
We need to find out the change in the amount of water after [tex]\(\frac{1}{3}\)[/tex] of an hour.
3. Calculate the change in the amount of water:
Since the water drains at [tex]\(-3.75\)[/tex] gallons per hour, we need to multiply this rate by the time period to find the total change. The calculation will be:
[tex]\[
\text{Change in water} = \text{Rate of change} \times \text{Time}
\][/tex]
Substituting the given values:
[tex]\[
\text{Change in water} = -3.75 \text{ gallons per hour} \times \frac{1}{3} \text{ hour}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Change in water} = -3.75 \times \frac{1}{3}
\][/tex]
5. Simplify the expression:
When you perform the multiplication:
[tex]\[
\text{Change in water} = -1.25 \text{ gallons}
\][/tex]
Therefore, the change in the amount of water in the bathtub after [tex]\(\frac{1}{3}\)[/tex] of an hour is [tex]\(-1.25\)[/tex] gallons. This means that 1.25 gallons of water has drained from the bathtub in that time span.
