Chapter 6.5, Problem 38E

a.

To determine

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

Answer to Problem 38E

The function that represents the number of people who have received the email after $n$ days is: $f(n)=6^n$

Explanation of Solution

Given:You start a chain email and send it to six friends. The next day, each of your friends forwards the email to six people. The process continues for a few days.

  

The function for a geometric sequence is:

  $f(n)=a_1{r}^{n-1}$

  $a_1=6$ , $r=6$

  $\begin{array}{l}f(n)=a_1{r}^{n-1}\\ $ f(n)=6{(6)}^{n-1}$f(n)=6^{1+n-1}\\ f(n)=6^n\end{array}$

Hence,

The function that represents the number of people who have received the email after $n$ days is: $f(n)=6^n$

b.

To determine

To find the days when 1296 people have received the email

Answer to Problem 38E

The function that represents the number of people who have received the email after $n$ days is: $f(n)=6^n$

Explanation of Solution

Given: You start a chain email and send it to six friends. The next day, each of your friends forwards the email to six people. The process continues for a few days.

  $\begin{array}{l}f(n)=1296\\ 6^n=1296\\ 6^n=6^4\\ n=4\end{array}$

Hence,

  $1296$ people have received the mails in 4 days.