Write an equation that shows the relationship between the number of months since Nicole founded the company, x, and the number of employees, y.
Understand the Problem
The question is asking for an equation that models the growth of employees in Nicole's company over time, based on the initial number of employees and the rate of hiring new employees each month.
Answer
The growth of employees can be modeled by the equation: $y = 6 + 4x$.
Answer for screen readers
The equation modeling the growth of employees is given by:
$$ y = 6 + 4x $$
Steps to Solve
-
Identify Initial Conditions
Nicole started her company with 6 employees. This gives us our starting point for the equation, where when $x = 0$ (the beginning), $y = 6$. -
Determine the Rate of Change
Nicole hires 4 new employees each month. This means that for every month that passes (for each unit increase in $x$), the number of employees ($y$) increases by 4. -
Formulate the Equation
To construct the equation, we can express the number of employees as a function of the number of months. The general formula will be: $$ y = \text{initial employees} + (\text{rate of hiring} \times x) $$
Plugging in the known values:
$$ y = 6 + 4x $$
The equation modeling the growth of employees is given by:
$$ y = 6 + 4x $$
More Information
This equation indicates that for every month that passes, the total number of employees increases linearly. Initially, there are 6 employees, and with 4 new hires each month, the number grows steadily.
Tips
- Failing to correctly interpret the initial count of employees. Remember that $x=0$ corresponds to the starting point.
- Confusing the rate of change with different units. Ensure that the rate of employee hiring is in the same time frame as $x$.
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