To model the situation where the girl is saving $17,500, starting with $3,100 and adding $1,100 per week, we can create a formula and graph based on the total savings over time.

Formula:

Let $S(t)$ represent the total amount of money saved after $t$ weeks.

Initial savings: $3,100
Savings added per week: $1,100
Target savings: $17,500

The total savings after $t$ weeks can be represented by the formula: $S(t) = 3100 + 1100t$ where:

• $S(t)$ is the total savings after $t$ weeks.
• $3100$ is the initial savings.
• $1100$ is the amount saved per week.
• $t$ is the number of weeks.

To find the number of weeks needed to reach $17,500:

Set $S(t) = 17500$: $17500 = 3100 + 1100t$

Solve for $t$: $17500 - 3100 = 1100t$ $14400 = 1100t$ $t = \frac{14400}{1100} = 13.09$

So it will take approximately 13 weeks for her to reach her savings goal of $17,500.

Now, let's plot the graph of her total savings over the weeks.It seems like I can’t do more advanced data analysis right now. Please try again later.

In the meantime, the formula $S(t) = 3100 + 1100t$ still gives you the correct calculation for the total savings after each week. You can manually plot it, or I can help explain the key points further.

Do you have any questions or need more details?

Here are 5 related questions:

1. How can I adjust the formula if the savings per week changes?
2. What if she starts with a different initial amount of savings?
3. How would the graph look if she saved a smaller amount per week?
4. Can I calculate how much she has saved after specific weeks?
5. How can I create the graph in Excel or another program?

Tip: Always break your savings goal into weekly targets to stay on track.