Math Problem Statement

a girl is saving 17500$, she has 3100$ and plans to save 1100$ per week, make formula and graph of every week

Solution

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

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

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

  • S(t)S(t) is the total savings after tt weeks.
  • 31003100 is the initial savings.
  • 11001100 is the amount saved per week.
  • tt is the number of weeks.

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

Set S(t)=17500S(t) = 17500: 17500=3100+1100t17500 = 3100 + 1100t

Solve for tt: 175003100=1100t17500 - 3100 = 1100t 14400=1100t14400 = 1100t t=144001100=13.09t = \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+1100tS(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.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Savings Models

Formulas

S(t) = 3100 + 1100t

Theorems

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Suitable Grade Level

Grades 6-8