The table shows the relationship between the amount of money (y) remaining in Maddy's money box and the number of months (x) : Function 1 Number of Months (x) Amount Remaining (in dollars) (y) 1 100 2 80 3 60 4 40 The equation shows the relationship between the amount of money (y) remaining in Caitlin's money box and the number of months (x) : Function 2: y = - 18x + 120 Which statement explains which function shows a greater rate of change? Function 2 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month. Function 2 shows a greater rate of change, because Maddy spends $100 each month and Caitlin spends $120 each month. Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends - $18 each month. Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month.

Question

Carissa

Mathematics

15 October, 10:21

The table shows the relationship between the amount of money (y) remaining in Maddy's money box and the number of months (x) : Function 1 Number of Months (x) Amount Remaining (in dollars) (y) 1 100 2 80 3 60 4 40 The equation shows the relationship between the amount of money (y) remaining in Caitlin's money box and the number of months (x) : Function 2: y = - 18x + 120 Which statement explains which function shows a greater rate of change? Function 2 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month. Function 2 shows a greater rate of change, because Maddy spends $100 each month and Caitlin spends $120 each month. Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends - $18 each month. Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month.

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Answers (1)

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Alexia Galvan · Answer 1

Maddie:

(1,100), (2,80)

slope (rate of change) = (80 - 100) / (2 - 1) = - 20/1 = - 20

Caitlin:

y = - 18x + 120 ... slope (rate of change) = - 18

To determine which rate of change is greater, take the absolute value of the slopes.

Maddy : | - 20 | = 20

Caitlin : | - 18 | = 18

the greater rate of change is the one with the larger absolute value ... so that would be Maddy ... function 1 shows a greater rate of change because Maddie spends 20 each month and Caitlin spends 18 each month