The cost $C(x)$, in dollars, of renting the moving truck for a day is modeled by the function:

$C(x) = 0.20x + 45$

where:

• $C(x)$ represents the total cost of renting the truck for a day,
• $x$ represents the number of miles driven,
• $0.20$ represents the cost per mile driven (in dollars),
• $45$ represents the fixed base cost for renting the truck, regardless of the miles driven.

This is a linear function where the fixed fee is $45$, and for each additional mile driven, there is a charge of $0.20$ dollars.

Example Calculation:

If you drive the truck for $100$ miles, the cost would be:

$C(100) = 0.20(100) + 45 = 20 + 45 = 65 \, \text{dollars}$

Would you like to explore more details or ask any further questions?

Here are 5 related questions to expand on this:

1. What is the cost if you drive 150 miles?
2. How would the function change if the base cost was $50 instead of $45?
3. How many miles can you drive if you have a budget of $100?
4. What is the cost per mile driven and how does it affect the total cost?
5. Can you graph the function $C(x)$ and interpret its slope and y-intercept?

Tip: The slope of a cost function like this represents the variable cost (per mile in this case), while the intercept is the fixed cost.