The cost​ C, in​ dollars, of renting a moving truck for a day is given by the function C(x) = 0.20x+45 where x is the number of miles driven.


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.

The cost​ C, in​ dollars, of renting a moving truck for a day is given by the function C(x) = 0.20x+45 where x is the number of miles driven.

Understand how to calculate the cost of renting a moving truck using the linear function C(x) = 0.20x + 45, where x represents the number of miles driven. Learn how the slope (0.20) represents the cost per mile and the y-intercept (45) represents the base cost. Suitable for students in Grades 8-10.

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