Chapter 1, Problem 15CR

To determine

To Estimate: the sales in fourth quarter of an e-commerce business.

Answer to Problem 15CR

  $\$2,20,000$

Explanation of Solution

Given:

Given that sales in second and third quarters is $\$170,000\text{and }\$\text{195,000}$ .

Calculation:

Let x be the quarters and y be the sales.

Since, sales are given in their respective quarters therefore it can be written in coordinate forms as.

  $\left(2,170000\right)\text{and }\left(3,195000\right)$

Slope of increment can be calculated as.

  $\begin{array}{l}\left(2,170000\right)\text{and }\left(3,195000\right)\\ m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{195000-170000}{3-1}\\ m=25,000\end{array}$

Equation in slope-intercept form can be written as.

  $y=mx+b$

Here, slope of increment of sales.

Substituting, $m=25,000$ , $x=2\text{and}y=170000$ in equation $y=mx+b$ .

  $\begin{array}{l}y=mx+b\\ 170000=25000\times 2+b\\ b=120,000\end{array}$

Therefore, equation for sales in terms of quarters is.

  $\begin{array}{l}y=mx+b\\ y=25000x+120000\end{array}$

Sales in fourth quarter is calculated by putting $x=4$ in above equation.

  $\begin{array}{l}y=25000x+120000\\ y=25000\times 4+120000\\ y=100,000+120,000\\ y=2,20,000\end{array}$

Therefore, the answer is $\$2,20,000$ .