The table shows the relationship between the amount of money (y) remaining in Lenny's money box and the number of months (x):

Function 1
Number of Months
(x) Amount Remaining (in dollars)
(y)
1 75
2 60
3 45
4 30

The equation shows the relationship between the amount of money (y) remaining in Thad's money box and the number of months (x):

Function 2:
y = −12x + 80

Which statement explains which function shows a greater rate of change?
Function 2 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.
Function 2 shows a greater rate of change, because Lenny spends $75 each month and Thad spends $12 each month.
Function 1 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.
Function 1 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $80 each month.

The answer is not Function 2 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.

Just so you know

Function 1 shows a greater rate of change, because Lenny spends $15 each month and Thad spends $12 each month.

The correct answer is: Function 2 shows a greater rate of change, because Lenny spends $75 each month and Thad spends $12 each month.

To determine which function shows a greater rate of change, we need to compare the changes in the amount of money (y) with respect to the number of months (x).

In Function 1, the amount of money decreases by $15 for each month that passes. In Function 2, the amount of money decreases by $12 for each month that passes.

Let's calculate the rate of change for each function:

Function 1: Change in y / Change in x = (-15 - 75) / (4 - 1) = -90 / 3 = -30
Function 2: Change in y / Change in x = (-12 - 80) / (1 - 0) = -92 / 1 = -92

From the calculations, we can see that the rate of change for Function 2 is -92, while the rate of change for Function 1 is -30.

Since the rate of change for Function 2 (-92) is greater than the rate of change for Function 1 (-30), we can conclude that Function 2 shows a greater rate of change.

Therefore, the correct statement is: "Function 2 shows a greater rate of change, because Lenny spends $12 each month and Thad spends $12 each month."