Chapter SH, Problem 9.10MPS

(a)

To determine

To calculate: To make a table showing the number of people that will have received the letter after $1,2,3,4$ stages.

Answer to Problem 9.10MPS

The table showing the number of people that will have received the letter is

Number of stage	Number of letters
1	3
2	9
3	27
4	81

Explanation of Solution

Given: The function $N=3^x$ represent total number of letters sent, where $x$ is the stage of letters

Calculation:

Given the function that represent total number of letters sent is

  $N=3^x$

When $x=1$

  $\begin{array}{l}N=3^1\\ N=3\end{array}$

When $x=2$

  $\begin{array}{l}N=3^2\\ N=9\end{array}$

When $x=3$

  $\begin{array}{l}N=3^3\\ N=27\end{array}$

When $x=4$

  $\begin{array}{l}N=3^4\\ N=81\end{array}$

Thus, table showing the number of people that will have received the letter is

Number of stage	Number of letters
1	3
2	9
3	27
4	81

Conclusion:

Hence, the table is constructed

(b)

To determine

To calculate: To graph the function

Explanation of Solution

Given: The table showing the number of people that will have received the letter is

Number of stage	Number of letters
1	3
2	9
3	27
4	81

Calculation:

Given the table showing the number of people that will have received the letter is

Number of stage	Number of letters
1	3
2	9
3	27
4	81

Plotting the points on graph:

Conclusion:

Hence, graph of function is plotted

(c)

To determine

To calculate: To find after how many stages will $243$ people receive the letter

Answer to Problem 9.10MPS

After $5$ stages $243$ people will receive the letter

Explanation of Solution

Given: The function $N=3^x$ represent total number of letters sent, where $x$ is the stage of letters

Calculation:

Given the function that represent total number of letters sent is

  $N=3^x$

In order to find the number of stages after which $243$ people will receive the letter, substitute $N=243$ in above equation:

  $\begin{array}{l}243=3^x\\ 3^x={\left(3\right)}^5\\ x=5\end{array}$

Conclusion:

Hence, after $5$ stages $243$ people will receive the letter