Final answer:
The growth of Greg's and Alan's companies can be compared by their linear equations: Greg's company grows by 18 employees each year, and Alan's grows by 22 employees per year. Alan's company is growing faster both initially and over time. Displaying this data graphically on a line graph would allow for easy visual comparison of their growth rates.
Step-by-step explanation:
The question asks us to compare the growth of two companies owned by Greg and Alan based on the equations provided for the number of employees over time. The equation for Greg's company is e = 18n + 5, and the equation for Alan's company is e = 22n + 10. Both equations show linear growth where the number of employees increases with each passing year. Greg's company adds 18 employees per year plus an initial count of 5, while Alan's company adds 22 employees per year with an initial count of 10.
By comparing the coefficients of n in each equation, Alan's company has a higher rate of growth in terms of employee counts because 22 is larger than 18. Furthermore, Alan's company starts with more employees. If we consider the growth of both companies in 10 years by plugging in n = 10 into their respective equations, we can see that Greg's company will have 18(10) + 5 = 185 employees and Alan's company will have 22(10) + 10 = 230 employees, confirming that Alan's company is growing at a faster pace.
To visualize these patterns and make numerical comparisons more easily, one might want to display data graphically. A line graph representing each company's growth would allow us to see the slope of each line and more quickly compare the two companies' growth rates. The steeper the slope, the faster the growth. This can help us build an intuitive grasp of the relationships and connections between the numbers.