Question

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

Answer 1

Answer:

$p_n = 135(1.05)^n$

Step-by-step 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

$(1+\frac{5}{100})$ each year, which is equivalent to

$(1+\frac{5}{100})=1.05$ 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.