Recent studies indicate that the average surface temperature...

Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function $T=0.02 t+8.50$, where $T$ is temperature in ${ }^{\circ} \mathrm{C}$ and $t$ represents years since 1900 . (a) What do the slope and $T$ -intercept represent? (b) Use the equation to predict the earth's average surface temperature in 2100 .

Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function $T=0.02 t+8.50$, where $T$ is temperature in ${ }^{\circ} \mathrm{C}$ and $t$ represents years since 1900 .
(a) What do the slope and $T$ -intercept represent?
(b) Use the equation to predict the earth's average surface temperature in 2100 .

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Key Concepts

Predictive Modeling

Predictive modeling using linear functions involves applying the established linear relationship to estimate future or unknown values of the dependent variable given new values of the independent variable. This approach is widely used in various fields to forecast trends and interpret potential outcomes based on historical or experimental data.

Intercept Interpretation

The y-intercept in a linear function is the value of the dependent variable when the independent variable is zero. It represents the starting point or initial condition of the model, serving as a baseline from which changes are measured.

Linear Function

A linear function represents a relationship between two variables in which the rate of change is constant. It is typically expressed in the form y = mx + b, where m is the slope and b is the y-intercept. This function provides a simplified model that can describe and predict trends in a wide range of real-world situations.

Slope Interpretation

The slope in a linear function indicates the rate at which the dependent variable changes with respect to the independent variable. It quantifies the change in the output for every one-unit increase in the input, providing insight into the strength and direction of the relationship between the two variables.

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