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

User Bex
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1 Answer

23 votes
23 votes

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(/ 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=(\ln 2)/(\ln 1.056)\approx12.72 \\ n=12.72+1=13.72 \end{gathered}

so, the tuition will be double after 13 years

User Addis
by
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