# Activities

• • • ##### Subject Area

• Math: Algebra I: Exponential Functions

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-89 / TI-89 Titanium
• TI-92 Plus / Voyage™ 200

TI Connect™

• ##### Accessories

CBL™/CBL 2™
Sensor - Temperature
TI Connectivity Cable

• ##### Report an Issue

Newton's Law Of Cooling and The Calculus Behind It

#### Activity Overview

In this activity, students investigate Newton's Law of Cooling and determine a model to represent the data.

#### Before the Activity

• Connect the temperature sensor to the DIG/SONIC port of the CBL 2™
• Connect the CBL 2™ to the calculator using the Unit-to-Unit cable
• Use the TI Connect™ software to transfer data from the computer to the calculator
• See the attached PDF file for detailed instructions for this activity
• Print pages from the attached PDF file for the class
• #### During the Activity

Distribute the pages to the class.

• Use calculus to derive the model for exponential growth and decay
• Understand that according to Newton's Law, if a chilled object warms to room temperature, the rate at which the object's temperature changes at any given time is proportional to the difference between its temperature and the temperature of the surrounding medium
• Collect temperature-time readings and use the Chill89 program to store the data
• Plot a graph and trace it to find the room temperature
• Study the standard exponential equation and use it to model the data
• Calculate the differences between the final and initial values for both data sets
• Use the calculator to perform exponential regression on the differences
• Derive the equation that models the original data
• Use the model to predict temperature at any given time
• #### After the Activity

Review student results.

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary