Question

joe’s friend gives him a $50 gift card for an online bookstore. each week joe purchases a digital book using his gift card. the amount of money left on his gift card after each week is shown in the table. is the rate of change constant or varying? how do you know?
how much does joe spend each week?
number of weeks, x | gift card balance ($), y
0 | 50.00
1 | 43.05
2 | 36.10
3 | 29.15
4 | 22.20

Explanation:

Step1: Calculate the difference in balance between week 0 and week 1

The balance at week 0 is $50.00 and at week 1 is $43.05. So the amount spent is $50.00 - $43.05 = $6.95.

Step2: Verify with other weeks (e.g., week 1 to week 2)

Balance at week 1: $43.05, at week 2: $36.10. Difference: $43.05 - $36.10 = $6.95.

Step3: Check another interval (week 2 to week 3)

Balance at week 2: $36.10, at week 3: $29.15. Difference: $36.10 - $29.15 = $6.95.

Step4: Confirm with week 3 to week 4

Balance at week 3: $29.15, at week 4: $22.20. Difference: $29.15 - $22.20 = $6.95.

Since the difference in balance (amount spent) is the same each week, the rate of change is constant, and Joe spends $6.95 each week.

Answer:

The rate of change (amount spent each week) is constant. We know this because the difference in the gift card balance between consecutive weeks is the same. Joe spends $6.95 each week.