Question

Each morning librarians place 560 books on a book shelf in the school library. Each student that visits library that day takes exactly 3 books from this shelf. Let s be the number of students which visit library on a particular day. Let b be the number of books left on the shelf at the end of that day.

b
There are 150 students studying in this school. Use this information to find the domain of the function b(s).

Answer 1

The domain of the function b(s) is

`s\in[0,150]`

Explanation:

Given that, a total of 560 books is added to the book shelf each morning.

`s` be the number of the students who visit the library on a particular day and takes exactly 3 books from this shelf.

So, the number of books they take from the shelf is 3s.

The number of remaining books the shelf
`=560-3s`.

As , given that
`b` be the number of books left on the shelf at the end of that day, so the required function,
`b(s)`, is

`b=560-3s\;\cdots(i)`

As there are 150 students in the school. So, if no one will go to the library, than
`s=0` which is the minimum value, and if all goes to the library , than
`s=150` which is the maximum value of
`s`.

So, the possible value of s is:

`0\leq s\leq150\;\cdots(ii)`

Now, as there is no book left or there are some books left the negative value of
`b` is not possible. So,

`b\geq0`

`\Rightarrow 560-3s\geq0` [fron equation (i)]

`\Rightarrow s\leq 560/3`

`\Rightarrow s\leq 186(2)/(3)`

as s id the number of students which cant be a fractional value, so the possible nearest value is,

`s\leq 186\;\cdots(iii)`

From the equations (ii) and (iii), the domain of the function
`b(s)` is

`s\in[0,150]`