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

Solve The number of people employed in the United States as registered nurses was $3,080,100$ in 2020 . By 2030, this number is expected to rise to $3,356,800$. Let $y$ be the number of registered nurses 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 registered nurses in year $x$. b. Use this equation to estimate the number of people employed as registered nurses in 2028 .

Solve
The number of people employed in the United States as registered nurses was $3,080,100$ in 2020 . By 2030, this number is expected to rise to $3,356,800$. Let $y$ be the number of registered nurses 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 registered nurses in year $x$.
b. Use this equation to estimate the number of people employed as registered nurses in 2028 .

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Key Concepts

Intercept

The intercept in a linear equation is the value of the dependent variable when the independent variable is zero. It serves as the starting point or initial value in the context of a linear model and is crucial for accurately predicting outcomes when the independent variable changes.

Estimation Using Linear Equations

Once a linear equation is established, it can be used to predict or estimate the value of the dependent variable for any given value of the independent variable. This involves substituting the desired value into the equation, allowing for forecasting based on the established linear trend.

Slope of a Linear Function

The slope represents the rate of change between the two variables in a linear equation, indicating how much the dependent variable increases or decreases for a unit change in the independent variable. It is calculated as the difference in the value of the dependent variable divided by the difference in the value of the independent variable.

Linear Modeling

This concept involves creating a mathematical representation of a relationship between two quantities that change at a constant rate. In this context, it means setting up a linear equation to model the number of registered nurses over time, where time is the independent variable and the number of nurses is the dependent variable.

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