Question

Lenny and Thad spend a certain amount of money from their money box each month to buy comic books.

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? (4 points)


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.

Answer 1

it is b

Step-by-step explanation:

Answer 2

Function 1, which represents Lenny's spending, shows a greater rate of change since Lenny spends $15 each month on comic books, compared to Thad, who spends $12 each month as indicated by the equation y = −12x + 80. The correct answer is option 3.

Step-by-step explanation:

To determine which function shows a greater rate of change, we examine how much money is spent each month from Lenny's and Thad's money boxes. Looking at Lenny's table (Function 1), we can see that the money decreases by $15 every month. For Thad's function (Function 2), the equation given is y = −12x + 80. The coefficient of x in Thad's equation represents the rate of change. Since the rate of change for Thad is −12, it indicates Thad spends $12 each month.

The function with the greater rate of change would be the function where the value decreases more quickly. Function 1, for Lenny, decreases by $15 each month, while Function 2, for Thad, decreases by $12 each month. Therefore, Function 1 shows a greater rate of change because Lenny spends $15 each month compared to Thad's $12 each month.