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)

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

1) The graph of this scenario would be a piecewise function because the rate of change changes. In the first 6 weeks, the rate of change is positive ($15 saved per week), and afterwards, the rate of change is negative ($10 spent per week).

2) The y-intercept of this graph would be $50, meaning at the start (week 0), Ryan already had $50.

3) The rate of change is negative (-$10) after the first 6 weeks because as the weeks increase, the money decreases at a constant rate of $10 spent per week.