Decay Functions



Problem 1 - Swinging Pendulum

The following table represents the swings of a pendulum. Complete the following information using your graphing calculator:


1.) Find the decay ratio in the above table. _______________________________________

2.) Use the graphing calculator to enter the data into two lists.

3.) Assuming that this is an exponential function, find the equation of best fit.
__________________________________________________________

4.) What is the domain of this function? ___________________________________________

5.) What is the range of this function? _____________________________________________

6.) What is the amplitude of the swing after 200 swings? ______________________________

7.) How many swings would it take to reach an amplitude of 10.2? ______________________

8.) Sketch the graph of this function.

Problem 2 - Cooling Function

Record the changing temperatures of a hot cup of coffee over the following time intervals:

1.) Find the decay ratio. __________________________________________________________________

2.) Use the graphing calculator to enter the data into the two lists.

3.) Assuming that this is an exponential function, find the equation of best fit.
______________________________________________________________

4.) What is the domain of this function? _____________________________________________________

5.) What is the range of this function? _______________________________________________________

6.) What would the temperature of the coffee be after 30 minutes? ________________________________

7.) How long would it take for the coffee to reach 37 degrees? ___________________________________


Submitted by Debbie Lancaster from Lakeside High School in Evans, GA.