Chapter 1.1, Problem 66AYU

Net Sales The figure illustrates the net sales growth of Costco Wholesale Corporation from $2013$ through $2017$. Use the midpoint formula to estimate the net sales of Costco Wholesale Corporation in $2015$. How does your result compare to the reported value of $\$113.67$ billion?

To determine

To calculate: The net sales of Costco Wholesale Corporation in $2015$ using the midpoint formula. Compare the result to the reported value of $\$113.67billion$

Answer to Problem 66AYU

Solution:

The estimated sales of Costco Wholesale Corporation in $2015$ is $114.52billion$

The reported value is $\$0.85$ billion off by the calculated value.

Explanation of Solution

Given Information:

The net sales of Costco Wholesale Corporation from $2013$ through $2017$ is as shown below

Formula used:

The midpoint formula: The coordinate of midpoint of two points $P_1=\left(x_1,y_1\right)$ and $P_2=\left(x_2,y_2\right)$ is $\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Calculation:

From the graph,

The net sales of Costco Wholesale Corporation in $2013$ is $\$102.87$ billion

The net sales of Costco Wholesale Corporation in $2017$ is $\$126.17$ billion

So, $P_1=\left(2013,102.87\right)$ and $P_2=\left(2017,126.17\right)$

By the midpoint formula, the coordinate of the midpoint of two points $P_1=\left(2013,102.87\right)$ and $P_2=\left(2017,126.17\right)$ is

$\left(x,y\right)=\left(\frac{2013+2017}{2},\frac{102.87+126.17}{2}\right)$

$\left(x,y\right)=\left(\frac{4030}{2},\frac{229.04}{2}\right)$

$\left(x,y\right)=\left(2015,114.52\right)$

So, the estimated sales of Costco Wholesale Corporation in $2015$ is $\$114.52\text{billion}$

The reported sales of Costco Wholesale Corporation in $2015$ is $\$113.67\text{billion}$

Therefore, the error in estimation $=|Reportedvalue-estimatedvalue|$

$=|113.67-114.52|$

$=0.85$

Therefore, the estimated sales of Costco Wholesale Corporation in $2015$ is $114.52billion$

The reported value is $\$0.85$ billion off by calculated value.