Saturday, April 16, 2016

College Algebra, Chapter 9, Review Exercises, Section Review Exercises, Problem 30

A teacher makes $35,000 in his first year, and gets a $1,200 raise each year.
a.) What is his salary An in his nth year at this school?
b.) Find his salary in his eighth year at this this school, and compare it to the salary of the teacher in her eighth year that makes $32,000 in her first
year and gets a 5% raise each year.

a.) Since the raise of the teacher is fixed at $1,200 each year, then the salary of the teacher can be represented by the criteria of
An=35,000+(n1)(1,200)

So the salary of the male teacher in his eight year is

A8=35,000+(81)(1,200)A8=$43,400


In the case of the female teacher, her salary for the first year is 32,000 while her salary for the year is 32,000+(0.05)32,000. Notice that,
the salary of the female teacher can be represented by the geometric sequence of

An=a(r)n1An=32,000(32,000+(0.05)(32,000)32,000)n1An=32,000(1.05\cancel(32,000)\cancel32,000)n1An=32,000(1.05)n1

Therefore, the salary of the female teacher on her eighth year is

A8=32,000(1.05)81A8=$45,027.21

It shows that the salary of the male teacher is initially higher than the salary of the female teacher. But, eventually the salary of the female
teacher will be higher since the increase in the salary of the male teacher is fixed.

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