Solve The number of people employed in the United States as...

Solve The number of people employed in the United States as secretaries or administrative assistants was $3,363,900$ in 2020. By 2030, this number is expected to fall to $3,137,700$. Let $y$ be the number of secretaries or administrative assistants employed in the United States in the year $x$, where $x=0$ represents 2020 . (Source: U.S Bureau of Labor Statistics) a. Write a linear equation that models the number of people employed as secretaries or administrative assistants in year $x$. b. Use this equation to estimate the number of people employed as secretaries or administrative assistants in 2027.

Solve
The number of people employed in the United States as secretaries or administrative assistants was $3,363,900$ in 2020. By 2030, this number is expected to fall to $3,137,700$. Let $y$ be the number of secretaries or administrative assistants employed in the United States in the year $x$, where $x=0$ represents 2020 . (Source: U.S Bureau of Labor Statistics)
a. Write a linear equation that models the number of people employed as secretaries or administrative assistants in year $x$.
b. Use this equation to estimate the number of people employed as secretaries or administrative assistants in 2027.

Key Concepts

Extrapolation

Extrapolation involves using the linear model to predict values outside the range of the given data. In the problem, after establishing the linear function based on historical data, the model is used to calculate the expected number of employees in a future year, such as 2027, by substituting x corresponding to that year into the equation.

Y-Intercept in Context

The y-intercept, represented by b in the equation y = mx + b, is the value of the function when x is zero. In this problem, x = 0 corresponds to the year 2020, so the y-intercept is the number of secretaries or administrative assistants employed in that base year. It establishes the starting point for the linear model.

Linear Functions

A linear function is a mathematical model that represents a constant rate of change between two variables, described by the equation y = mx + b. In the context of the problem, it is used to model how the number of secretaries or administrative assistants changes over time, assuming that the change between years is uniform.

Slope of the Linear Equation

The slope, denoted by m in the linear equation, represents the rate of change in the dependent variable (number of workers) with respect to the independent variable (time). In real-world applications like this, the slope tells us how many positions are lost or gained per year, reflecting the overall trend over the period.

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