Question

A large company created a phonetree to contact all employees incase of an emergency. Each ofthe five vice presidents calls fiveemployees, who in turn each call five other employees, and soon. How many rounds of phonecalls are needed to reach all 2375employees?

Answer 1

Given:

Number of vice presidents are =5 ,

And number of employees are 2375 ,

They cotenct each of the five employees and turn to next five ,

The sequence of the terms will be a geometric sequence ,

`5,25,125,\ldots\ldots2375`

Hnce the number of terms are ,

`t_n=t_1r^(n-1)`

In the series the common ratio is r=5,

And t1=5 and tn= 2375 therefore ,

`\begin{gathered} 2375=5*5^(n-1) \\ 5^(n-1)=(2375)/(5) \\ 5^(n-1)=475 \\ \end{gathered}`

Taking log on both side ,

`\begin{gathered} (n-1)\log 5=\log 475 \\ n-1=(\log 475)/(\log 5) \\ n=1+(2.676)/(0.698) \\ n=4.829 \end{gathered}`

Hence the approximate value of the number of rounds is 5.