To solve the problem of finding the average rate of change in gas price from 3 to 6 predicted storms, we need to use the following steps:
1. Identify the prices at the specific storms:
- From the table, we see that the gas price when 3 storms are predicted is [tex]$2.44.
- Additionally, the price when 6 storms are predicted is $[/tex]2.56.
2. Calculate the change in price:
- Subtract the gas price at 3 storms from the gas price at 6 storms: [tex]\( 2.56 - 2.44 \)[/tex].
3. Calculate the change in the number of storms:
- Subtract the number of storms at the beginning of the period (3) from the number at the end of the period (6): [tex]\( 6 - 3 \)[/tex].
4. Calculate the average rate of change:
- Divide the change in gas price by the change in the number of storms:
[tex]\[
\frac{\Delta \text{Price}}{\Delta \text{Storms}} = \frac{(2.56 - 2.44)}{(6 - 3)}
\][/tex]
Now, let's perform these steps with the given values:
1. The change in gas price:
[tex]\[
2.56 - 2.44 = 0.12
\][/tex]
2. The change in the number of storms:
[tex]\[
6 - 3 = 3
\][/tex]
3. The average rate of change:
[tex]\[
\frac{0.12}{3} = 0.04
\][/tex]
So, the average rate of change in gas price from 3 to 6 predicted storms is [tex]\( \$0.04 \)[/tex] per storm.
