Let's determine the percent change in the person's income from [tex]$27,000 to $[/tex]40,000.
1. Identify the initial and final values:
- Initial income: [tex]$27,000
- Final income: $[/tex]40,000
2. Calculate the change in income:
[tex]\[
\text{Change in income} = \text{Final income} - \text{Initial income} = 40,000 - 27,000 = 13,000
\][/tex]
3. Determine the percent change:
[tex]\[
\text{Percent change} = \left( \frac{\text{Change in income}}{\text{Initial income}} \right) \times 100 = \left( \frac{13,000}{27,000} \right) \times 100
\][/tex]
4. Calculate the percent change:
[tex]\[
\text{Percent change} \approx 48.15\%
\][/tex]
Since the person's income has increased, and we calculated the percent change to be approximately 48.15%, the correct answer is:
[tex]\[
\boxed{48.15\% \text{ increase}}
\][/tex]
