https://file.aiquickdraw.com/mathbot/file/17281505499612f1wnhcm.jpg

Let's break this down step-by-step.

### Part a) What type of function would best model this situation?
Since the problem involves spending a constant amount of $23 per week on gas, the relationship between the amount spent and the number of weeks would be linear. The amount of money remaining on the gift card decreases by a fixed amount each week, which is characteristic of a linear function.

- **Answer:** Linear

### Part b) Write a function to model this situation (use $ w $ for the number of weeks).
You start with $240 on the gift card, and each week you spend $23. The total amount of money left after $ w $ weeks can be modeled by the function:

\[
g(w) = 240 - 23w
\]

Here, $ 240 $ is the starting amount, and $ 23w $ is the total spent after $ w $ weeks.

### Part c) Evaluate $ g(4) $.
To evaluate $ g(4) $, substitute $ w = 4 $ into the function:

\[
g(4) = 240 - 23(4) = 240 - 92 = 148
\]

So, after 4 weeks, you would have $148 left on the gift card.

---

Would you like further explanation or details on any part of this?

### 5 Related Questions:
1. What would the function look like if the weekly gas cost increased by $5 each week?
2. How many weeks will it take to use up the entire $240 gift card?
3. What happens to the graph of the function if you start with a different gift card amount?
4. How can you use this function to determine how much gas money is left after any number of weeks?
5. What if you decide to only spend $15 per week? How would that change the function?

### Tip:
Always check whether the relationship between variables is constant when determining if the situation is linear. A constant rate of change indicates linearity.

Suppose you have a $240 gift card for gas, and you average $23 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(4).

Learn how to model gas expenses with a $240 gift card and $23 weekly gas usage. This algebra problem uses linear functions and substitution to evaluate the remaining balance after 4 weeks. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation