Let's break this down into two parts: finding Aaron's salary after 6 years, and then creating an expression for his salary after $t$ years.

Part 1: Salary after 6 years

Aaron's initial salary is $52,000, and each year he receives a $3,500 raise. After 6 years, his salary can be calculated using the formula:

$\text{Salary after 6 years} = 52000 + 3500 \times 6$

Now, let's do the calculations:

$\text{Salary after 6 years} = 52000 + 21000 = 73000$

So, Aaron's salary after 6 years would be $73,000.

Part 2: General formula for salary after $t$ years

To find Aaron's salary after any number of years $t$, we use the same method. Each year, his salary increases by $3,500. Therefore, the expression for his salary after $t$ years is:

$\text{Salary after } t \text{ years} = 52000 + 3500 \times t$

Where:

• $52000$ is his starting salary.
• $3500$ is the annual raise.
• $t$ is the number of years he has worked.

So, after $t$ years, Aaron's salary would be:

$52000 + 3500t$

Summary

• Aaron's salary after 6 years: $73,000.
• Salary after $t$ years: $52000 + 3500t$.

Would you like to see more details or have any further questions?

Here are 5 related questions to further explore this topic:

1. How much would Aaron's total earnings be after working for 6 years?
2. If Aaron's annual raise increased to $4,000, how would his salary after 6 years change?
3. How many years would it take for Aaron's salary to double his starting salary?
4. What would be the effect of an initial salary of $60,000 on his salary after $t$ years?
5. If the raises were given every 6 months instead of annually, how would this affect his salary growth?

Tip: In problems involving sequences, identifying patterns or increments is key to forming general expressions.