Question

The annual tuition at a community college since 2001 is modeled by the equation C = 2000(1.08)n, where C is the tuition cost and n is the number of years since 2001.

a) What was the tuition cost in 2001?


b) What is the annual percentage of tuition increase?

c.) Find the tuition cost in 2006.

Answer 1

Answer: a) $2000 b) 8% c)$2,938.66

Explanation:

Given: The annual tuition at a community college since 2001 is modeled by the equation
`C=2000(1.08)^n`, where C is the tuition cost and n is the number of years since 2001.

It is exponential growth equation
`y=A(1+r)^n`, where

a)The initial cost (at year 2001) A= 2000

⇒ The tuition cost in 2001 = $ 2,000

b)The rate of growth= 0.08 or 8%

⇒ The annual percentage of tuition increase = 8%

c) To find the tuition cost in 2006, put n=5 in the equation ( Since n= 2006-2001=5), we get

The tuition cost in 2006=
`C=2000(1.08)^5=2938.656\approx2938.66`

Hence, the tuition cost in 2006= $2,938.66