Chapter 6.6, Problem 38E

a.

To determine

To Write: The function that represents the number of people who have received the email after n days..

Answer to Problem 38E

The function is $y(n)=6^n$

Explanation of Solution

Given information: You start a chain email and send it to six friends. Next day, each of your friends forwards it to 6 people. The process continues.

Calculation:

First day you 1 sent to 6 friends

Next day 6 sent to 686 =36 friends

Third day 36 sent to 36*6=216 friends

So, sequence would be like 1,6,36, 216,….

Let’s find the rule for this

First term is 1, second term is 6, third term is 6², fourth term is 6³, ….

Here first term is 1, it could be written as 6⁰

So, the rule is

  $y(n)=6^n$

b.

To determine

To Find: After how many days the 1296 people reached the mail.

Answer to Problem 38E

It would take 4 days to reach 1296 people.

Explanation of Solution

Given information: The function $y(n)=6^n$

Calculation:

Plug in y(n) as 1296.

It gives $1296=6^n$

Take log on both sides

  $log\left(1296\right)=\left(n\right)log6$

Divide both sides by log 6

  $\begin{array}{l}log\left(6^4\right)=\left(n\right)log6\\ \Rightarrow 4\log 6=n\log 6\\ \Rightarrow n=4\end{array}$

Therefore, it would take 4 days to reach 1296 people.