Activity Detail
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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.

    Follow the Activity procedures:
  • 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

    		Other Downloads




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    Subject Area:
    Math : Algebra I : Linear Equations and Functions

    Author:
    Texas Instruments

    Level:
    9-12

    Activity Time:
    60 Minutes

    Device:
    TI-89 / TI-89 Titanium, TI-92 Plus / Voyage™ 200

    Apps:
    DataMate

    Software:
    TI Connect™

    Accessories:
    CBL™/CBL 2™, Sensor - Temperature, TI Connectivity Cable, Unit-to-Unit link cables

    Other:
    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


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