To determine when the rate of change in the amount Mr. Barnett spent on gas was greatest, we need to compare the differences in the amounts spent between consecutive months.
First, let's calculate the rate of change between April and May:
- Amount spent in April: [tex]\( \$87 \)[/tex]
- Amount spent in May: [tex]\( \$93 \)[/tex]
The rate of change between April and May is calculated as follows:
[tex]\[
\text{Rate of change (April to May)} = \text{Amount in May} - \text{Amount in April} = 93 - 87 = 6
\][/tex]
Next, let's calculate the rate of change between June and July:
- Amount spent in June: [tex]\( \$57 \)[/tex]
- Amount spent in July: [tex]\( \$72 \)[/tex]
The rate of change between June and July is calculated as follows:
[tex]\[
\text{Rate of change (June to July)} = \text{Amount in July} - \text{Amount in June} = 72 - 57 = 15
\][/tex]
Comparing the two rates of change, we find:
- Rate of change between April and May: [tex]\( 6 \)[/tex]
- Rate of change between June and July: [tex]\( 15 \)[/tex]
Therefore, the rate of change was greater between June and July.
