The table of values below represents a linear function and shows the amount of money in Juanita’s savings account since she began her part-time job. What is her monthly rate of savings?

Question

Amount in Juanita’s Savings Account
Number of Months Working at Part-Time Job
0
2
4
6
8
Amount in Savings Account (in dollars)
$36
$60
$84
$108
$132
$12 per month
$18 per month
$24 per month
$36 per month

GPT-4o mini · Answer

To find Juanita's monthly rate of savings, we need to determine the amount of money she saves for each month she works.

We can look at the values given for the amount in the savings account:

At 0 months: $36
At 2 months: $60
At 4 months: $84
At 6 months: $108
At 8 months: $132

First, we can take any two consecutive points and find the difference in the amount saved over the difference in months.

Let's calculate the savings between the first two points (0 months and 2 months):

Amount at 2 months: $60
Amount at 0 months: $36

Change in amount = $60 - $36 = $24
Change in months = 2 - 0 = 2

Now, we can calculate the monthly rate of savings: \[ \text{Monthly Rate} = \frac{\text{Change in amount}}{\text{Change in months}} = \frac{24}{2} = 12 \text{ dollars per month} \]

We can check this with the next periods (2 to 4 months and so on) to confirm:

From 2 months ($60) to 4 months ($84): $ 84 - 60 = 24 $ in 2 months, so again $ 12 $ dollars per month.
From 4 months ($84) to 6 months ($108): $ 108 - 84 = 24 $ in 2 months, so again $ 12 $ dollars per month.
From 6 months ($108) to 8 months ($132): $ 132 - 108 = 24 $ in 2 months, so again $ 12 $ dollars per month.

The pattern shows that the savings are increasing consistently.

Thus, Juanita's monthly rate of savings is $12 per month.