To determine the average rate of change in miles per hour during the interval from 0.75 to 1.00 hours, we can follow these steps:
1. Identify the given data points:
- At [tex]\( t = 0.75 \)[/tex] hours, the distance traveled is [tex]\( 3.50 \)[/tex] miles.
- At [tex]\( t = 1.00 \)[/tex] hours, the distance traveled is [tex]\( 4.75 \)[/tex] miles.
2. Use the formula for the average rate of change:
[tex]\[
\text{Average rate of change} = \frac{\Delta \text{Distance}}{\Delta \text{Time}}
\][/tex]
Where [tex]\(\Delta\)[/tex] represents the change in the respective quantities.
3. Calculate [tex]\(\Delta \text{Distance}\)[/tex] and [tex]\(\Delta \text{Time}\)[/tex]:
- Change in Distance ([tex]\(\Delta \text{Distance}\)[/tex]):
[tex]\[
\Delta \text{Distance} = \text{Distance at } t = 1.00 \text{ hours} - \text{Distance at } t = 0.75 \text{ hours}
\][/tex]
[tex]\[
\Delta \text{Distance} = 4.75 \text{ miles} - 3.50 \text{ miles} = 1.25 \text{ miles}
\][/tex]
- Change in Time ([tex]\(\Delta \text{Time}\)[/tex]):
[tex]\[
\Delta \text{Time} = 1.00 \text{ hours} - 0.75 \text{ hours} = 0.25 \text{ hours}
\][/tex]
4. Substitute the changes into the formula:
[tex]\[
\text{Average rate of change} = \frac{1.25 \text{ miles}}{0.25 \text{ hours}}
\][/tex]
5. Perform the division:
[tex]\[
\frac{1.25 \text{ miles}}{0.25 \text{ hours}} = 5.00 \text{ miles per hour}
\][/tex]
Thus, the average rate of change in miles per hour during the interval from 0.75 to 1.00 hours is [tex]\( 5.00 \)[/tex] miles per hour.
The correct answer is:
5.00 miles per hour
