In 1993, the life expectancy at birth of males was 72.2...

In $1993,$ the life expectancy at birth of males was 72.2 years. In $2006,$ it was 75.1 years. Let $E$ represent life expectancy and $t$ the number of years since 1990 Source: National Vital Statistics Reports a) Find a linear equation that fits the data. b) Predict the life expectancy of males in 2010 .

In $1993,$ the life expectancy at birth of males was 72.2 years. In $2006,$ it was 75.1 years. Let $E$ represent life expectancy and $t$ the number of years since 1990 Source: National Vital Statistics Reports
a) Find a linear equation that fits the data.
b) Predict the life expectancy of males in 2010 .

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Key Concepts

Extrapolation

Extrapolation involves using a linear model to predict values outside the range of the data used to construct the model. This technique assumes that the established trend continues beyond the known data, which is useful for forecasting future outcomes, albeit with potential uncertainty.

Y-intercept

The y-intercept is the point where the graph of the linear equation crosses the y-axis, meaning it is the value of the dependent variable when the independent variable is zero. In practical applications, it often represents the initial condition or starting value in a modeled scenario.

Slope

The slope in a linear equation represents the rate of change between the two variables. It quantifies how much the dependent variable (often represented by y) changes for a one-unit increase in the independent variable (x). Understanding the slope is essential in determining trends and relationships in data.

Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable raised to the first power. In many contexts, including modeling real-world phenomena, a linear equation takes the form y = mx + b, where m is the slope and b is the y-intercept, allowing for straightforward interpretation and prediction.

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