Chapter 9.2, Problem 85E

a.

To determine

To construct: The bar graph showing the annual sales from 2004 through 2011.

Answer to Problem 85E

  

Explanation of Solution

Given: The table shows the sales $a_n$ (in billions of dollars) for Eli Lilly and Co. from 2004 through 2011.

  $\begin{array}{ccccccccc}\text{Year}& 2004& 2005& 2006& 2007& 2008& 2009& 2010& 2011\\ \text{Sales }{a}_n& 13.9& 14.6& 15.7& 18.6& 20.4& 21.8& 23.1& 24.3\end{array}$

Now, draw the bar graph of sales $a_n$ .

Where, sales, $a_n$ represents on $y-$ axis and year, $n$ represents on $x-$ axis.

Sales shows height of bar graph.

  

b.

To determine

To find: An arithmetic sequence of the annual sales from 2004 through 2011.

Answer to Problem 85E

  $a_n=11.1+0.7n$

Explanation of Solution

Given: The table shows the sales $a_n$ (in billions of dollars) for Eli Lilly and Co. from 2004 through 2011.

  $\begin{array}{ccccccccc}\text{Year}& 2004& 2005& 2006& 2007& 2008& 2009& 2010& 2011\\ \text{Sales }{a}_n& 13.9& 14.6& 15.7& 18.6& 20.4& 21.8& 23.1& 24.3\end{array}$

Let $n$ represents the year, with $n=4$ corresponding to 2004.

Since $n=4$ corresponding to 2004.

  $\therefore a_4=13.9$ and $a_5=14.6$

The data of the table is in arithmetic sequence. The common difference, $d=a_5-a_4$

  $\therefore d=14.6-13.9=0.7$

  $\begin{array}{c}{a}_4=a+3d\\ 13.9=a+3\left(0.7\right)\\ a=11.8\end{array}$

The models which shows table data.

  $\begin{array}{l}{a}_n=11.8+\left(n-1\right)0.7\\ a_n=11.1+0.7n\end{array}$

c.

To determine

To graph: The table data.

Answer to Problem 85E

  

Explanation of Solution

Given: The table shows the sales $a_n$ (in billions of dollars) for Eli Lilly and Co. from 2004 through 2011.

  $\begin{array}{ccccccccc}\text{Year}& 2004& 2005& 2006& 2007& 2008& 2009& 2010& 2011\\ \text{Sales }{a}_n& 13.9& 14.6& 15.7& 18.6& 20.4& 21.8& 23.1& 24.3\end{array}$

Let $n$ represents the year, with $n=4$ corresponding to 2004.

The given is ${\displaystyle \sum _{j=1}^{200}\left(10.5+0.025j\right)}$

The $n^{\text{th}}$ term is $a_n=11.1+0.7n$ .

Now, draw the graph of $a_n=11.1+0.7n$ .

Where, $a_n$ represents on $y-$ axis and $n$ represents on $x-$ axis.

  

d.

To determine

To find: The sum of total sales from 2004 through 2011.

Answer to Problem 85E

152.4 billion dollars

Explanation of Solution

Given: The table shows the sales $a_n$ (in billions of dollars) for Eli Lilly and Co. from 2004 through 2011.

  $\begin{array}{ccccccccc}\text{Year}& 2004& 2005& 2006& 2007& 2008& 2009& 2010& 2011\\ \text{Sales }{a}_n& 13.9& 14.6& 15.7& 18.6& 20.4& 21.8& 23.1& 24.3\end{array}$

Let $n$ represents the year, with $n=4$ corresponding to 2004.

The given is ${\displaystyle \sum _{j=1}^{200}\left(10.5+0.025j\right)}$

The $n^{\text{th}}$ term is $a_n=11.1+0.7n$ .

The total sum, ${\displaystyle \sum _{n=4}^{11}{a}_n}$

Total sales, $S=a_4+a_5+a_6+a_7+a_8+a_9+a_{10}+a_{11}$

  $\begin{array}{l}S=13.9+14.6+15.7+18.6+20.4+21.8+23.1+24.3\\ S=152.4\end{array}$

Hence, the total sales 152.4 billion dollars in 8 years.