Ryan is tracking how much money he has each week.

Question

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
nonlinear
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

Let's break down the components of Ryan's scenario:

1. Type of Graph: The graph of this scenario would be nonlinear because the rate of change changes. For the first 6 weeks, Ryan is saving $15 per week (a linear increase). After week 6, he starts spending $10 per week (a linear decrease). However, since these two segments of the graph have different behaviors, the overall trajectory of the graph is considered piecewise linear, which is nonlinear when taken as a whole.

2. Y-Intercept: The y-intercept of this graph would be $50, meaning this is the amount of money Ryan has at the start (week 0).

3. Rate of Change After the First 6 Weeks: The rate of change is -10 dollars per week after the first 6 weeks because as the weeks increase, the money decreases by $10 each week until it runs out.

Putting it all together:

1. Nonlinear
2. $50 (this is the starting amount)
3. -10 dollars per week