Precalculus: How Cool It Is

Objectives

• Students will determine and analyze an exponential model for the temperature of water as it cools.
• Students will make predictions about the time required to reach various water temperatures and about the water temperature at various times.

Vocabulary

• exponential function
• regression equation
• sum of squares due to error

About the Lesson

This lesson involves creating an exponential regression equation to model the temperature of water as it cools.

As a result, students will:

• Learn how to adjust their equation to produce an equation that will better model the data.
• Adjust their equation to incorporate the fact that water will not get cooler than the temperature of the room..
• Use sliders to change the values of the variables a and b in their model to produce the smallest SSE (the Sum of Squares due to Error) value.