Suppose you have a $220 gift card for gas. You spend on average $25 per week for gas.

a) Write a function to model this situation where 
 is the number of weeks and g(w) is the value in dollars remaining on the card.


We are given a $220 gift card for gas and a weekly gas expenditure of $25. Let $ w $ represent the number of weeks, and $ g(w) $ represent the value remaining on the gift card after $ w $ weeks.

### To model this situation:

1. **Initial amount on the card:** $ 220 $ dollars.
2. **Weekly gas expenditure:** $ 25 $ dollars per week.

The remaining balance on the card after $ w $ weeks will decrease by $ 25 $ dollars for each week. Therefore, the function $ g(w) $ representing the remaining balance is:

\[
g(w) = 220 - 25w
\]

### Explanation:
- $ g(w) $ is the remaining balance on the gift card after $ w $ weeks.
- $ 220 $ is the initial balance.
- $ 25w $ represents the total amount spent after $ w $ weeks, so we subtract it from the initial balance.

Would you like further clarification or more details on how to use this function?

Here are 5 related questions to expand on this:
1. How many weeks will it take to completely use up the gift card?
2. What will be the balance after 6 weeks of gas spending?
3. How would the function change if you spent $30 per week instead of $25?
4. What if you spent different amounts on gas each week? How would you model that situation?
5. How would the graph of this function look like?

**Tip:** Always check the domain of a function—here, the number of weeks $ w $ must be non-negative, and the gift card balance can't be less than zero!

Suppose you have a $220 gift card for gas. You spend on average $25 per week for gas. a) Write a function to model this situation where w is the number of weeks and g(w) is the value in dollars remaining on the card.

Learn how to model the gas expenditure using a $220 gift card. This problem uses linear functions and algebra to find the remaining balance after spending $25 per week on gas. Suitable for students in Grades 6-8, it covers key concepts like linear equations and function modeling.

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