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