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. a How does the number of books left on the shelf depend on number of students visiting library? Find formula for the function b(s).

Answer:The domain of the function b(s) is[tex]s\in[0,150][/tex]Step-by-step explanation:Given that, a total of 560 books is added to the book shelf each morning.[tex]s[/tex] 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 [tex]=560-3s[/tex].As , given that [tex]b[/tex] be the number of books left on the shelf at the end of that day, so the required function, [tex]b(s)[/tex], is[tex]b=560-3s\;\cdots(i)[/tex]As there are 150 students in the school. So, if no one will go to the library, than [tex]s=0[/tex] which is the minimum value, and if all goes to the library , than [tex]s=150[/tex] which is the maximum value of [tex]s[/tex].So, the possible value of s is:[tex]0\leq s\leq150\;\cdots(ii)[/tex]Now, as there is no book left or there are some books left the negative value of [tex]b[/tex] is not possible. So,[tex]b\geq0[/tex][tex]\Rightarrow 560-3s\geq0[/tex] [fron equation (i)][tex]\Rightarrow s\leq 560/3[/tex][tex]\Rightarrow s\leq 186\frac{2}{3}[/tex]as s id the number of students which cant be a fractional value, so the possible nearest value is,[tex]s\leq 186\;\cdots(iii)[/tex]From the equations (ii) and (iii), the domain of the function [tex]b(s)[/tex] is[tex]s\in[0,150][/tex]