The CEO of a start-up technology company was interested in the rapid growth of his company and employees. A table is given with the data collected in the first year of business.
\begin{tabular}{|l|l|}
\hline Months & Total Employees \\
\hline 0 & 4 \\
\hline 1 & 5 \\
\hline 2 & 8 \\
\hline 3 & 11 \\
\hline 4 & 15 \\
\hline 5 & 20 \\
\hline 6 & 27 \\
\hline 7 & 34 \\
\hline 8 & 42 \\
\hline 9 & 54 \\
\hline 10 & 65 \\
\hline 11 & 79 \\
\hline 12 & 93 \\
\hline
\end{tabular}
Based on the data, what does the slope of the best model of fit tell us about the relationship of the months and the total number of employees in the company?
The predicted number of total employees in the company is increasing by 8.7 for each increase in one month
The predicted number of total employees in the company is increasing by 73 for each increase in one month.
The predicted number of total employees in the company are multiplied by an additional factor of 4.7 for each increase in one month.
The predicted number of total employees in the company are multiplied by an additional factor of 1.3 for each increase in one month.
Answer
\(\boxed{\text{The predicted number of total employees in the company is increasing by approximately 7.42 for each increase in one month.}}\)
Step 1 ：Given the data of months and total employees, we are asked to find the slope of the best fit line. The slope of the line in this context represents the rate of change of the total number of employees with respect to time (months).
Step 2 ：We can calculate the slope between each consecutive pair of points using the formula for the slope of a line, which is \((y2 - y1) / (x2 - x1)\).
Step 3 ：Calculate the differences between consecutive months and employees: \[diff\_months = [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\] \[diff\_employees = [1, 3, 3, 4, 5, 7, 7, 8, 12, 11, 14, 14]\]
Step 4 ：Calculate the slopes between each consecutive pair of points: \[slopes = [1, 3, 3, 4, 5, 7, 7, 8, 12, 11, 14, 14]\]
Step 5 ：Calculate the average slope by summing up all the slopes and dividing by the number of slopes: \[average\_slope = \frac{\sum slopes}{\text{number of slopes}} = \frac{1+3+3+4+5+7+7+8+12+11+14+14}{12} = 7.42\]
Step 6 ：\(\boxed{\text{The predicted number of total employees in the company is increasing by approximately 7.42 for each increase in one month.}}\)
