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

Answer:

The domain of the function b(s) is

$s\in[0,150]$

Step-by-step 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)]

$\Rightarrow s\leq 560/3$

$\Rightarrow s\leq 186\frac{2}{3}$

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

$s\in[0,150]$