Let's go through the detailed steps to understand the cost function and how it calculates the total cost of renting a moving van.
1. Understanding the Cost Function:
The given cost function is:
[tex]\[
c(x) = 0.50x + 25
\][/tex]
where:
- [tex]\(x\)[/tex] represents the number of miles driven.
- [tex]\(0.50\)[/tex] is the cost per mile in dollars.
- [tex]\(25\)[/tex] is the fixed rental cost in dollars.
2. Identify Fixed and Variable Costs:
- Fixed Cost: The fixed cost of renting the moving van is \[tex]$25.00. This is a flat fee that you pay regardless of how many miles you drive.
- Variable Cost: The variable cost per mile is \$[/tex]0.50. This means for every mile you drive, you will incur an additional cost of \[tex]$0.50.
3. Calculate the Total Cost for a Given Number of Miles:
If you want to find out the total cost for driving a specific number of miles, you plug in that value into the cost function. For example, let us assume you drive 10 miles.
4. Substitute the Number of Miles into the Cost Function:
Using \(x = 10\):
\[
c(10) = 0.50 \times 10 + 25
\]
5. Perform the Calculations:
- First, calculate the variable cost:
\[
0.50 \times 10 = 5.00
\]
- Then, add the fixed cost:
\[
5.00 + 25 = 30.00
\]
6. Result:
The total cost of renting the moving van and driving 10 miles is \$[/tex]30.00.
To summarize:
- The fixed rental cost is \[tex]$25.00.
- The cost per mile is \$[/tex]0.50.
- For driving 10 miles, the total cost will be \$30.00.
