We have been given that the number of books in a small library increases according to the function [tex]B =5400e^{0.02t}[/tex], where t is measured in years. We are asked to find the number books in the library after nine years.
To find the number books in the library after nine years, we will substitute [tex]t=9[/tex] in our given equation as:
[tex]B =5400e^{0.02(9)}[/tex]
[tex]B =5400e^{0.18}[/tex]
[tex]B =5400(1.1972173631218102)[/tex]
[tex]B =6464.973760857[/tex]
Upon rounding to nearest whole number, we will get:
[tex]B\approx 6465[/tex]
Therefore, there will be approximately 6465 books in the library after 9 years.
