Question

A college's tuition of $135 per credit hour increases by 5% each year

Answer 1

`p_n = 135(1.05)^n`

Explanation:

In the situation of this problem, we have:

- The initial college's tuition per hour is

`p_0 = 135\$`

- Then, we know that the price increases by 5% each year. This means that its value increases by

`(1+(5)/(100))` each year, which is equivalent to

`(1+(5)/(100))=1.05` each year

So, after 1 year, the price will be

`p_1 = 1.05 p_0`

After 2 year, the price will be

`p_2 = 1.05 p_1 = 1.05(1.05 p_0)=1.05^2 p_0`

So after n years, the price will be

`p_n = 1.05^n p_0`

And by substituting the value of p0, we find the final expression:

`p_n = 135(1.05)^n`

where n is the number of years.