The graph below shows the distance in miles, m, hiked from a camp in h hours. Which hourly interval had the greatest rate of change?

1) hour 0 to hour 1
3) hour 2 to hour 3
2) hour 1 to hour 2
4) hour 3 to hour 4

The greatest rate of change between the interval 0 to 1 hour.

Given that,

The graph below shows the distance in miles, m, hiked from a camp in h hours.

We have to determine,

Which hourly interval had the greatest rate of change?

According to the question,

The greatest rate of change between the interval is determined by the rate of change between two points refers to the vertical change divided by the horizontal change.

1. The rate of change between 0 to 1 hours is,

The rate of change between 0 to 1 hour is 2.

2. The rate of change between 2 to 3 hours is,

The rate of change between 2 to 3 hours is 1.

3. The rate of change between 1 to 2 hours is,

The rate of change between 1 to 2 hours is 1.5.

4. The rate of change between 3 to 4 hours is,

The rate of change between 2 to 3 hours is 1.

Hence, The required greatest rate of change between the interval 0 to 1 hour.

For more details refer to the link given below.

link

Option 1) is correct

Step-by-step explanation:

Given: The graph shows the distance in miles, m, hiked from a camp in h hours.

To find: hourly interval that had the greatest rate of change

Solution:

Rate of change between two points refers to the vertical change divided by the horizontal change.

For hour 0 to hour 1:

rate of change =

For hour 2 to hour 3:

rate of change =

For hour 1 to hour 2:

rate of change =

For hour 3 to hour 4:

rate of change =

So, rate of change is greatest in interval: hour 0 to hour 1