Question

If tuition at a college is increasing by 5.6% each year, how many years will it take for tuition to double?

Answer 1

Given:

The tuition at a college is increasing by 5.6% each year

Let the tuition = a

So, the increases every year will form a geometric sequence

The first term = a

And the common ratio = r = 1.056

And the general term will be:

$a_n=a\cdot r^{n-1}$

We will find the value of (n) at the term (2a)

$\begin{gathered} 2a=a\cdot1.056^{n-1}\rightarrow(\div a) \\ 2=1.056^{n-1} \end{gathered}$

Taking the natural logarithm to both sides

$\begin{gathered} \ln 2=(n-1)\cdot\ln 1.056 \\ n-1=\frac{\ln 2}{\ln 1.056}\approx12.72 \\ n=12.72+1=13.72 \end{gathered}$

so, the tuition will be double after 13 years