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A software company started off with 2 employees. They added 2 new employees every 8 months. Which equation shows the relationship between the number of employees y and the number of months x since the company started?

a) y = 0.25x + 2
b) y = 0.5x + 2
c) y = 8x + 2
d) y = 2x + 8

User Davey
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1 Answer

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Final answer:

The correct equation to describe the relationship between the number of employees y and the number of months x since the company started is y = 0.25x + 2, option (a). This reflects the initial count of 2 employees and an addition of 2 employees every 8 months.

Step-by-step explanation:

To find the equation that shows the relationship between the number of employees y and the number of months x since the company started, we need to determine the rate at which new employees are added and the initial number of employees.

The company starts with 2 employees, which is our initial value for y when x is 0. Since they add 2 new employees every 8 months, the rate of change in number of employees is 2 employees per 8 months. To find the slope (the rate at which employees increase per month), we divide the number of employees added by the time period: 2 employees / 8 months = 0.25 employees per month. This slope tells us how much the number of employees increases for each month that passes.

Therefore, the equation that represents this situation is y = 0.25x + 2, which correlates with option (a). Here the slope is 0.25, indicating the rate of employee increase per month, and the y-intercept is 2, indicating the initial number of employees.

User Nommer
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