# 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

• ##### Other Materials
This is Activity 6 from the EXPLORATIONS Book:
Discovering Math on the Voyage 200.

The following material is required for this acttivity:
• A cup of hot water
• ##### Report an Issue

Warming Up to Heating Curves

#### Activity Overview

In this activity, students use the CBL 2™ to collect temperature data as a sensor warms up in a cup of water. They find an appropriate mathematical model for the resulting data set.

#### Before the Activity

• Connect the calculator to the CBL 2 unit using the link cables
• Connect the temperature sensor into channel 1 of the CBL 2 unit and start the DataMate program
• See the attached PDF file for detailed instructions for this activity
• Print pages 41 - 47 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Place the temperature sensor in a cup of hot water and collect temperature versus time data
• Model the temperature data using a modified exponential function y = a(1 - b^x) + c where x = time and y = temperature
• Find c (the starting temperature), and y (the approach temperature)
• Solve for the value of a
• Use different values of b and find a value of b such that it gives a graph that best fits the data generated
• Use the DataMatrix editor to perform an exponential regression
• Verify if the values of a and b match those from the model
• Plot the regression curve and compare it with the modeling curve to find how well the equation fits the data
• #### After the Activity

Review student results:

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