Question

The number of books donated to a library is increasing by 25% each month. Initially, there were 80 books donated to the library. There were 100 books donated at the end of Month 1.

How many books are expected to be donated to the library at the end of Month 10?



Round the answer to the nearest whole number.

Answer 1

Answer:

745 books

Step-by-step explanation:

This is a compound growth problem since the 25% increase is on each and every year.

The formula for compound growth is:

$A=P(1+\frac{r}{100})^{t}$

Where,

• A is the future value of something
• P is the initial value
• r is the growth rate
• t is the time (each unit)

For our problem, it is given that initial value (P) is 80, rate of growth (r) is 25, and we want to find number of books after 10 months, so time (t) is 10. Substituting these values, gives us:

$A=80(1+\frac{25}{100})^{10}\\A=80(1+0.25)^{10}\\A=80(1.25)^{10}\\A=745.06$

Rounding to nearest whole number, we conclude that after Month 10, there would be about 745 books in the library.