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 [tex]$y$[/tex] and the number of months [tex]$x$[/tex] since the company started?

A. [tex]$y=0.5 x+2$[/tex]
B. [tex]$y=8 x+2$[/tex]
C. [tex]$y=0.25 x+2$[/tex]
D. [tex]$y=2 x+8$[/tex]

Question

A. [tex]$y=0.5 x+2$[/tex]
B. [tex]$y=8 x+2$[/tex]
C. [tex]$y=0.25 x+2$[/tex]
D. [tex]$y=2 x+8$[/tex]

GinnyAnswer · Answer

The problem describes a linear relationship between the number of employees and the number of months. The company starts with 2 employees, and the number of employees increases by 0.25 every month. Therefore, the equation is: 
 
 The initial number of employees is 2. 
 The rate of change is 8 2 ​ = 0.25 . 
 The equation is in the form y = m x + b , where m is the rate of change and b is the initial number of employees. 
 The equation is y = 0.25 x + 2 ​ . 
 
 Explanation 
 
 Problem Analysis Let's analyze the problem. We are given that a software company starts with 2 employees and adds 2 new employees every 8 months. We need to find the equation that represents the relationship between the number of employees y and the number of months x since the company started. 
 
 Initial Employees The company initially has 2 employees. This is the y-intercept of the equation, so the equation will be in the form y = m x + 2 , where m is the slope. 
 
 Rate of Change The company adds 2 employees every 8 months. This means the rate of change (slope) is 8 months 2 employees ​ = 4 1 ​ = 0.25 employees per month. 
 
 Equation Therefore, the equation that represents the relationship between the number of employees y and the number of months x is y = 0.25 x + 2 .

Examples 
 Imagine you are tracking the growth of a plant. You start with a plant that is 2 inches tall, and it grows 0.25 inches every month. The equation y = 0.25 x + 2 can help you predict the height of the plant ( y ) after a certain number of months ( x ). This type of linear equation is useful for modeling growth or decline over time in various real-world scenarios.

Anonymous · Answer

The equation that represents the relationship between the number of employees y and the number of months x since the company started is y = 0.25 x + 2 . This represents an initial 2 employees with an increase of 0.25 employees per month. Therefore, the correct answer is option C: y = 0.25 x + 2 . 
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Answer (2)

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