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Let's analyze and solve this question step by step:

### Problem Overview
- You have a $180 gift card for gas.
- You spend $25 per week on gas.

#### a) Type of function that would best model this situation:
- This is a **Linear** function because you are consistently spending $25 per week, which means the amount left on the card decreases at a constant rate.

#### b) Writing the function:
Let $ g(w) $ represent the amount of money left on the card after $ w $ weeks. Since you start with $180 and spend $25 each week, the function will be:

\[
g(w) = 180 - 25w
\]

Where:
- $ 180 $ is the starting amount (the initial gift card balance),
- $ 25w $ is the amount spent after $ w $ weeks.

#### c) Evaluate $ g(3) $:
To find the amount left after 3 weeks, plug $ w = 3 $ into the function:

\[
g(3) = 180 - 25(3) = 180 - 75 = 105
\]

So, after 3 weeks, there will be $105 left on the gift card.

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Do you have any questions or want further details on any of these steps?

### Relative Questions:
1. How would the function change if you increased the weekly gas spending?
2. What would happen if you started with a different initial gift card amount?
3. Can you find the number of weeks after which the gift card balance becomes $0?
4. What is the graphical interpretation of this linear function?
5. How would the function differ if the spending was not consistent every week?

**Tip:** Linear functions always change by a constant amount, making them easy to model situations with consistent rates.

Suppose you have a $180 gift card for gas, and you average $25 per week in gas. a) What type of function would best model this situation? b) Write a function to model this situation (Use w for number of weeks). c) Evaluate g(3).

Learn how to model a $180 gas card balance with linear functions, where $25 is spent per week. Step-by-step solution with function writing and evaluation for 3 weeks.

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