Solve each problem. (Modeling) Online Retail SalesProjected retail e-commerce sales (in billions of dollars) for the years 2016–2022 can be modeled by the equation y=52.304x+396.80, where x=0 corresponds to 2016, x=1 corresponds to 2017, and so on. Based on this model, find projected retail e-commerce sales in 2022 to the nearest tenth of a billion. (Data from www.statista.com)

Key Concepts

Linear Equations

A linear equation is an algebraic expression that represents a straight line when graphed. It typically takes the form y = mx + b, where m is the slope and b is the y-intercept. In this context, the equation y = 52.304x + 396.80 models the relationship between the year and projected sales, allowing us to predict future values based on the linear trend.

Slope and Intercept

The slope of a linear equation indicates the rate of change of the dependent variable (y) with respect to the independent variable (x). In the given equation, the slope is 52.304, meaning that for each year increase (x), the projected sales increase by approximately 52.304 billion dollars. The y-intercept, 396.80, represents the projected sales when x equals 0, or the year 2016.

Modeling and Predictions

Modeling in mathematics involves creating a representation of a real-world situation using equations. In this case, the equation models online retail sales over a specific period. By substituting the appropriate value of x (which corresponds to the year 2022, or x=6), we can predict the sales for that year, demonstrating how mathematical models can be used for forecasting in business.