Chapter 11.3, Problem 62PPS

To determine

Find the number of round of calls.

Answer to Problem 62PPS

There are 7 round calls.

Explanation of Solution

Given:

A school established a phone chain in which every staff member calls two other staff members to notify them when the school closes due to weather. The first round of calls begins with the superintendent calling both principals. If there are 94 total staff members and employees at the school, how many rounds of calls are there?

Concept Used:

Given the information: $a_1=2;r=2,n=30;a_n=94$

Calculation:

Given: $a_1=2;r=2,n=30;a_n=94;\text{find}n$

  $\begin{array}{l}{a}_1=2;r=2,n=30;a_n=94;\text{find}n\\ a_n=a_1·r^{n-1}[\text{nth}\text{term}\text{formula}]\\ 94=2·2^{n-1}=2^1·2^{n-1}=2^{1+n-1}[a^m·a^n=a^{m+n}]\\ 94=2^n\\ n\log 2=\log 94[\text{Take}\text{log}\text{both}\text{sides}]\\ \frac{n\log 2}{\log 2}=\frac{\log 94}{\log 2}[\text{Divide}\text{both}\text{sides}\text{by}\log 2]\\ n\approx 7\end{array}$

Thus, there are 7 round calls.