Question
number of gallons pumped (4,15) and (8, 30) what is the rate of change in the cost of each gallon as it is pumped
Answers
Answered by
GPT-4o mini
To determine the rate of change in the cost per gallon as it is pumped, we can interpret the points (4, 15) and (8, 30) as follows:
- The first point (4, 15) means that when 4 gallons are pumped, the cost is $15.
- The second point (8, 30) means that when 8 gallons are pumped, the cost is $30.
The rate of change in the cost per gallon can be calculated by finding the change in cost divided by the change in the number of gallons pumped between these two points.
1. Calculate the change in cost:
\[
\Delta \text{Cost} = \text{Cost at 8 gallons} - \text{Cost at 4 gallons} = 30 - 15 = 15
\]
2. Calculate the change in gallons:
\[
\Delta \text{Gallons} = \text{Gallons at 8} - \text{Gallons at 4} = 8 - 4 = 4
\]
3. Now, calculate the rate of change in cost per gallon:
\[
\text{Rate of Change} = \frac{\Delta \text{Cost}}{\Delta \text{Gallons}} = \frac{15}{4} = 3.75
\]
Thus, the rate of change in the cost per gallon as it is pumped is $3.75 per gallon.
- The first point (4, 15) means that when 4 gallons are pumped, the cost is $15.
- The second point (8, 30) means that when 8 gallons are pumped, the cost is $30.
The rate of change in the cost per gallon can be calculated by finding the change in cost divided by the change in the number of gallons pumped between these two points.
1. Calculate the change in cost:
\[
\Delta \text{Cost} = \text{Cost at 8 gallons} - \text{Cost at 4 gallons} = 30 - 15 = 15
\]
2. Calculate the change in gallons:
\[
\Delta \text{Gallons} = \text{Gallons at 8} - \text{Gallons at 4} = 8 - 4 = 4
\]
3. Now, calculate the rate of change in cost per gallon:
\[
\text{Rate of Change} = \frac{\Delta \text{Cost}}{\Delta \text{Gallons}} = \frac{15}{4} = 3.75
\]
Thus, the rate of change in the cost per gallon as it is pumped is $3.75 per gallon.