Question

TutorialMona currently brings in an annual salary of $81,000 and anticipates a raise of 5% everyyear. What will her salary be in 10 years?

Answer 1

We are given that Mona's salary will increase 5% annually every year. This is a case of exponential growth. The general form of the exponential equation for exponential growth is the following:

`y=a(1+r)^x`

Where:

`\begin{gathered} a=\text{ initial value} \\ r=\text{ rate of growth in decimal form} \end{gathered}`

In this case, the variable "y" is the salary and the variable "x" is the time.

First, we will convert the rate of growth into decimal form. We do this by dividing the rate by 100:

`r=(5)/(100)=0.05`

Now we substitute in the equation:

`y=81000(1+0.05)^x`

Solving the operation inside the parenthesis we get:

`y=81000(1.05)^x`

Now we substitute the value of "x = 10" to determine the salary "y" after 10 years:

`y=81000(1.05)^(10)`

Solving the operations:

`y=131940.47`

Therefore, the salary after 10 years is $131940.47