Question

The first month a company was open, it had 2 employees. At the end of 6 months the company had 10 employees. If the number of employees increases at a steady rate, write an equation that illustrates this situation

Answer 1

The situation of a company starting with 2 employees and growing to 10 employees over a 6-month period at a steady rate is represented by the equation E = (4/3)m + 2, where E is the number of employees and m is the number of months.

Step-by-step explanation:

To write an equation that illustrates the situation where a company started with 2 employees and increased to 10 employees over 6 months at a steady rate, we need to determine the rate of increase.

Let's assume that the number of employees (E) depends on the number of months (m) the company has been open. We are given two points: (0, 2) and (6, 10), where the first element of each pair is the time in months, and the second is the number of employees.

The slope (rate of increase) can be calculated using the slope formula, which is the change in the number of employees divided by the change in time. The slope (m) is therefore (10 - 2) / (6 - 0) = 8 / 6 = 4 / 3.

So the company is adding 4/3, or approximately 1.33, employees every month.

The equation representing this situation can be written in the slope-intercept form as E = mt + b, where E is the number of employees, m is the slope, and b is the y-intercept (the number of employees at month 0, which is 2).

Hence, the equation is:

E = (4/3)m + 2