To determine in which year Joe's income reached \[tex]$38,200, let's break the problem step by step.
1. Initial Income and Income in the 5th Year:
- Joe’s income in the 1st year = \$[/tex]22,900
- Joe’s income in the 5th year = \[tex]$26,500
2. Calculate the Annual Increase in Income:
- We know the increase in income over 4 years (from the 1st year to the 5th year).
- Increase in income over 4 years = \$[/tex]26,500 - \[tex]$22,900 = \$[/tex]3,600
- Annual increase in income = \[tex]$3,600 / 4 = \$[/tex]900
3. Set Up the Equation to Find the Target Year:
- Suppose Joe's income reaches \[tex]$38,200 in the nth year.
- The formula to calculate annual income given the yearly increase is:
\[
\text{Yearly Income} = \text{Initial Income} + (\text{Year} - 1) \times \text{Annual Increase}
\]
- We need to find \(n\) such that:
\[
38,200 = 22,900 + (n - 1) \times 900
\]
4. Solve the Equation for \(n\):
- Rearrange the equation:
\[
38,200 = 22,900 + 900(n - 1)
\]
- Subtract 22,900 from both sides:
\[
15,300 = 900(n - 1)
\]
- Divide both sides by 900:
\[
17 = n - 1
\]
- Add 1 to both sides:
\[
n = 18
\]
Therefore, Joe's income was \$[/tex]38,200 in the 18th year.
So, the answer is:
Joe's income was \$38,200 in the 18th year.
