This problem describes an arithmetic sequence for the hourly salary.

We know:

• First year's salary: $a_1 = 8.50$
• Second year's salary: $a_2 = 8.85$

In an arithmetic sequence, the difference between consecutive terms is constant. This difference $d$ can be found as: $d = a_2 - a_1 = 8.85 - 8.50 = 0.35$

The explicit rule for an arithmetic sequence is given by: $a_n = a_1 + (n - 1)d$ Substituting the values: $a_n = 8.50 + (n - 1)(0.35)$ This is the explicit formula for the hourly salary for year $n$.

Would you like further explanation on how this formula was derived or applied?

Here are 5 related questions to further explore:

1. What would the hourly salary be in the third year using this formula?
2. How would the sequence change if the annual increase was different?
3. Can you apply this formula to find the salary in year 10?
4. How does the difference $d$ affect the steepness of salary growth?
5. What if this was a geometric sequence instead of an arithmetic one?

Tip: In any arithmetic sequence, the key to solving is identifying the first term and the common difference!