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

First, lets create a equation for our situation. Let $x$ be the months. We know four our problem that Eliza started her savings account with $100, and each month she deposits $25 into her account. We can use that information to create a model as follows:
$f(x)=25x+100$

We want to find the average value of that function from the 2nd month to the 10th month, so its average value in the interval [2,10]. Remember that the formula for finding the average of a function over an interval is: $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1} }$. So lets replace the values in our formula to find the average of our function:
$\frac{25(10)+100-[25(2)+100]}{10-2}$
$\frac{350-150}{8}$
$\frac{200}{8}$
$25$

We can conclude that the average rate of change in Eliza's account from the 2nd month to the 10th month is $25.