https://file.aiquickdraw.com/mathbot/file/17278797112398t7gg449.jpg

Let's break this down and solve each part of the problem:

### a) What type of function would best model this situation?

- You start with a gift card worth $230 and spend $15 per week. This is a **linear situation** because the amount you spend per week is constant (a fixed $15 every week). Therefore, the function is **Linear**.

### b) Write a function to model this situation. 

- Let $ g(w) $ represent the remaining balance on the gift card after $ w $ weeks.
- The initial balance is $230, and each week you spend $15. Therefore, after $ w $ weeks, you will have spent $ 15w $, and the remaining balance will be $ 230 - 15w $.

Thus, the function is:
\[
g(w) = 230 - 15w
\]

### c) Evaluate $ g(4) $

- To find $ g(4) $, substitute $ w = 4 $ into the function $ g(w) $:
\[
g(4) = 230 - 15(4) = 230 - 60 = 170
\]
So, after 4 weeks, the remaining balance on the gift card is $170.

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Would you like more details or have any questions on this? Here are 5 related questions to expand your understanding:

1. What would happen to the function if you spent a different amount per week?
2. How would the graph of $ g(w) $ look, and what does the slope represent?
3. What does the y-intercept of the function $ g(w) $ represent in this context?
4. How many weeks would it take for the gift card balance to reach $0?
5. What would $ g(w) $ look like if you added $50 to the gift card after 3 weeks?

**Tip:** Linear functions represent situations where there is a constant rate of change, which is common in everyday spending scenarios like this one!

Suppose you have a $230 gift card for gas, and you average $15 per week in gas. a) What type of function would best model this situation? b) Write a function to model this situation. c) Evaluate g(4).

This problem demonstrates how to model gas spending with a $230 gift card using a linear function. The function g(w) = 230 - 15w shows the remaining balance after spending $15 per week. Perfect for students in Grades 6-8 learning about linear relationships and algebraic functions.

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