Question

At the beginning of the year, the number of books owned by a library was 10,000. Since then, it has grown by 1% each month.Which expressions represent the number of books, in thousands, owned by the library 5 years later if it continues to grow at that rate? •(101)^60 •(1+0.01/12)^60 •(1.01)^5 •(0.01)^60 •((1+0.01)^12)^5

Answer 1

ANSWER

$10(1+\frac{0.01}{12})^{60}$

EXPLANATION

We want to find the expression that represents the number of books after 5 years.

To do this, we have to apply the general formula for the amount of an exponential increase based on a 12 month time period:

$a(1+\frac{r}{12})^{12\cdot x}$

where P = initial amount

r = rate

x = amount of time (number of years)

From the question:

P = 10,000

r = 1% = 0.01

t = 5 years

Therefore, the expression that represents the number of books (in thousaands) after 5 years is:

$\begin{gathered} 10(1+\frac{0.01}{12})^{12\cdot5} \\ \Rightarrow10(1+\frac{0.01}{12})^{60} \end{gathered}$

That is the answer.