A library has a collection of 4200 books in 2016 Through a g

A library has a collection of 4200 books in 2016. Through a generous grant, each year on Jan.1 the librarian will purchase enough additional books to increase the collection by 8%. Determine how many books the library will have in 2026. Please show all work

Solution

Each year purchase causes the colloection to increase by 8%

2016 : 1st year = 4200

2017 2nd year =4200(1+8/100)

2018 3rd year = 4200( 1+8/100)(1 +8/100) = 4200( 1+8/100)^2

General function for no. of books the libraray will have after x years: 4200( 1+8/100)^x

F(x) = 4200( 1+8/100)^x where x = no. of years

In 2026 : x= 10 years

No.of books in collection = 4200( 1+8/100)^10 = 4200*(1.08)^10 = 9067 books ( taking whole numbers only)