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The price of gas has been increasing over the last month. Renee believes there is a positive correlation between the number of predicted storms and the price of gas.

| Number of Storms Predicted | Gas Price |
|----------------------------|-----------|
| 1 | [tex]$2.34 |
| 3 | $[/tex]2.44 |
| 4 | [tex]$2.49 |
| 6 | $[/tex]2.56 |
| 7 | $2.61 |

Use the table to determine the average rate of change from 3 to 6 storms.

A. 0.04
B. 0.12
C. 0.27


Sagot :

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.
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