Question

Eliza started her savings account with $100. Each month she deposits $25 into her account. Determine the average rate of change in Eliza's account from the 2nd month to the 10th month. Show all work for full credit.

Answer 1

$25 per month

Explanation:

f(x) = 100 + 25x x = number of months

In two month, the amount will be:

f(2) = 100 + 25(2)

f(2) = 100 + 50

f(2) = 350

In ten months, the amount will be:

f(10) = 100 + 25(10)

f(10) = 100 + 250

f(10) = 350

The average rate of change from the second month to the tenth month will be:

f(10) - f(2)/10-2

= 350 - 150/8

= 200/8

= 25

So the average rate of change will be $25 per month.

Answer 2

"Each month she deposits $25 into her account" tells me that the average rate of change from the 2nd to the 10th month is simply $25/month. Of course you can calculate this using the "average rate of change formula"

f(b) - f(a)
ave r of c = ---------------------
b - a

Here f(x) = $100 + ($25)x, a = 2 and b = 10