carly receives $50 every week for babysitting for her neighbors. she decides to save the money she receives to help pay for a camp she wants to attend next summer. she tracks how much money she saves from babysitting over the course of the year...

Question

explain why carly savings over time is an example of linear change? carly saving over time is an example of linear change because you are adding $50 every week.

Create a sequence that describes carlys growing saving each week over the course of 8 weeks.

create a formula for carlys savings over time.. y=___

use your formula and find the amount carly has saved after 1 year (hint 52 weeks in a year..)
after 52 weeks carly has saved ___

Answer 1

Carly's savings over time is indeed an example of linear change because she consistently adds the same amount of money ($50) to her savings every week. This means her savings grow at a constant rate, which is the hallmark of a linear relationship.

Sequence of Carly’s Savings Over 8 Weeks:

1. Week 1: $50
2. Week 2: $100
3. Week 3: $150
4. Week 4: $200
5. Week 5: $250
6. Week 6: $300
7. Week 7: $350
8. Week 8: $400

So the sequence is: $50, $100, $150, $200, $250, $300, $350, $400

Formula for Carly's Savings Over Time:

Let \( y \) represent the total savings and \( x \) represent the number of weeks. Since Carly adds $50 each week, the formula will be: \[ y = 50x \]

Amount Saved After One Year (52 Weeks):

Using the formula: \[ y = 50x \]

Substituting \( x = 52 \): \[ y = 50 \times 52 \] \[ y = 2600 \]

So, after 52 weeks, Carly has saved $2,600.