Question

Ryan is tracking how much money he has each week.He started with $50.He saves $15 per week for the first 6 weeks.He spent $10 per week after week 6 until the money's all spent.(4 points)1) The graph of this scenario would be because the rate of change changes.2) The y-intercept of this graph would be meaning .3) The rate of change is after the first 6 weeks because as the weeks increase the money decreases.

Answer 1

The graph of this scenario would be______ because the rate of change changes. linear or non

The y-intercept of this graph would be______ meaning__________ first part answers are 0,10, 0,50 0,5 second part is ryan started with $10, ryan started with $50, and ryan started a 6 weeks

The rate of change is________ after the first 6 weeks because as the weeks increase the money decreases. answers are negtive and positive

Answer 2

Let's break down each point related to Ryan's financial situation:

1) **The graph of this scenario would be a piecewise function or a step function** because the rate of change changes. For the first 6 weeks, Ryan's money increases due to his savings, and then after week 6, it decreases because of his spending. Thus, the graph will have a linear increase for the first 6 weeks and then a linear decrease afterwards.

2) **The y-intercept of this graph would be $50, meaning this is the amount of money Ryan started with.** The y-intercept represents the initial amount of money he has before any savings or spending occurs.

3) **The rate of change is negative after the first 6 weeks because as the weeks increase, the money decreases.** Initially, for the first 6 weeks, the rate of change is positive (+$15 per week). However, after week 6, Ryan begins to spend money, leading to a negative rate of change (-$10 per week).

### Summary of Calculation
- **Initial amount:** $50
- **Savings for first 6 weeks:** $15/week → Total after 6 weeks = $50 + (6 × $15) = $50 + $90 = $140
- **Spending after 6 weeks:** $10/week from week 7 onwards. Starting from $140:
- After week 7: $140 - $10 = $130
- After week 8: $130 - $10 = $120
- Continuing until the money is all spent.

This gives a clear structure to Ryan's spending and savings, as well as the graphical representation of his financial situation.

Answer 3

Here are the answers based on your scenario:

1) **The graph of this scenario would be non-linear** because the rate of change changes.

2) **The y-intercept of this graph would be 0, $50**, meaning **Ryan started with $50**.

3) **The rate of change is negative** after the first 6 weeks because as the weeks increase, the money decreases.

### Summary
1) Non-linear (due to changes in rate)
2) 0, $50; meaning Ryan started with $50
3) Negative (because his money decreases after week 6)