Question

Maddy and Caitlin spend a certain amount of money from their money box each month to buy bracelet-making supplies.

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                   Amount remaining (in $)
(x)                                                          (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?


A: Function 2 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month.

B: Function 2 shows a greater rate of change, because Maddy spends $100 each month and Caitlin spends $120 each month.

C: Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends −$18 each month.

D: Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month.

Answer 1

D

The answer is d

Answer 2

The appropriate choice is ...
D: Function 1 shows a greater rate of change, because Maddy spends $20 each month and Caitlin spends $18 each month.

_____
Each time the month number in Function 1 goes up by 1, the account balance goes down by $20. Each time the month number in Function 2 goes up by 1, the account balance goes down by $18. Once you have figured out that $20 is more than $18, you know the first two answers cannot be right. The third answer is wrong because Caitlin cannot (and does not) spend -$18 each month.