Question

53. Every year, Mikhail receives a 3% raise in his annual salary. His starting annual salary was $40,000.

a. Does a geometric or arithmetic sequence best model Mikhail’s salary in yearn? Explain how you know.

Answer 1

Geometric sequence.

Explanation:

In this situation Mikhail's salary increases by a constant multiple each year. A 3% rate is equivalent to multiplying the previous salary by a constant of 1.03, Mikhail's salary can be modeled by the following recursive equation:

`S_(n)=S_(n-1)*1.03`.

Therefore, since the same multiple can be used to find the next term in the sequence, a geometric sequence best models his salary.