Final answer:
Option 2, the 3% raise each year, models exponential growth. After year 1, the $1000 increase earns more money. After year 7, a comparison involving cumulative income is required to determine which option earns more.
Step-by-step explanation:
The problem given involves understanding the difference between linear growth and exponential growth, as well as comparing the outcomes of these two types of growth over time. Let's analyze each option.
Exponential Growth
Option 2, which provides a 3% raise each year, models exponential growth. This is because each year the raise is dependent on the previous year's salary, meaning the amount of the raise increases as the base salary increases.
Comparison After Year 1
After the first year, the increase of $1000 results in a higher salary compared to a 3% increase. This is because 3% of the starting salary of $3800 equals $114, which is less than a $1000 increase.
Comparison After Year 7
The more money earned after year 7 would depend on the cumulative effect of the raises. It requires a comparison of the total income after 7 years for both options. A graph or a calculator can be useful in comparing these two options over time to determine which one yields a higher cumulative salary.