Chapter 9.2, Problem 77E

(a)

To determine

To Find: The bar graph for that shows the annual net numbers of new stores opened by H and M from 2011 through 2015.

Answer to Problem 77E

The required graph is shown in Figure 1

Explanation of Solution

Given:

The given data is shown in Table 1

Table 1

Year	New Stores
2011	266
2012	304
2013	356
2014	379
2015	413

Calculation:

From, the given data the required graph is shown in Figure 1

  

Figure 1

(b)

To determine

To Find: The nth term of the arithmetic sequence that approximate the data. Let n represent the year with $n=1$ that corresponds to 2011.

Answer to Problem 77E

The required model is $a_n=266+\left(n-1\right)36.75$ .

Explanation of Solution

Consider the formula for the nth term of the sequence is,

  $a_n=a_1+\left(n-1\right)d$

Then,

  $\begin{array}{c}{a}_n=266+\left(n-1\right)\left(\frac{413-266}{5-1}\right)\\ =266+\left(n-1\right)36.75\end{array}$

(c)

To determine

To Find: The graphing utility to graph the terms of the finite sequence found in part (b).

Answer to Problem 77E

The graph for the model is shown in Figure 2

Explanation of Solution

Consider the given model is,

  $a_n=266+\left(n-1\right)36.75$

Then, the graph for the above model is shown in Figure 2

  

Figure 2

(d)

To determine

To Find: The total number of new stores opened from 2011 through 2015 and use the sum to approximate the total number of new stores opened during the year.

Answer to Problem 77E

The number of stores is $1698$ .

Explanation of Solution

Consider the summation to be done is,

  ${\displaystyle \sum _{n=1}^5\left(229.25+36.75\right)}$

Then, the formula for the sum of finite arithmetic sequence is,

  $\begin{array}{c}{S}_n=\frac{n}{2}\left(a_1+a_n\right)\\ =\frac{5}{2}\left(266+413\right)\\ =1698\text{stores}\end{array}$