oliver is starting a business. he brought a pressure washer for $460. he will charge $25 a hour and spend $2/hr on gas. what is the function that models Oliver's expenses

To model Oliver's expenses, we need to consider both the fixed cost (the initial cost of the pressure washer) and the variable cost (the cost of gas per hour).

1. **Fixed Cost:** The initial cost of the pressure washer is $460.
2. **Variable Cost:** The cost of gas is $2 per hour, and let's denote the number of hours he works as $ h $.

So, the total expense function $ E(h) $, where $ h $ is the number of hours, is given by:

\[
E(h) = 460 + 2h
\]

This function $ E(h) = 460 + 2h $ models Oliver's total expenses based on the number of hours he works.

Would you like further details or have any questions? Here are some related questions to consider:

1. How would you model Oliver's revenue?
2. At how many hours of work will Oliver cover his expenses?
3. What is the profit function for Oliver's business?
4. How does the expense function change if gas prices increase to $3 per hour?
5. How would the expenses change if Oliver buys an additional tool?

**Tip:** Always separate fixed and variable costs when modeling business expenses to easily analyze and predict future costs.

Learn how to model Oliver's business expenses using a linear function. This problem involves understanding fixed and variable costs, represented by the equation E(h) = 460 + 2h. Suitable for students in Grades 6-8, this example provides insights into cost analysis in a business context.

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