Mr. Tadros & Ms. Woodhull love math ~ so you should to!!!
Introduction
How many licks does it take to get to the center of a tootsie pop?
Task
Who doesn't enjoy a tootsie pop?
Have you ever realized as you are eating it, that your tootsie pop is getting smaller and smaller?
Have you ever wondered how fast it's shrinking?
Well today is your lucky day!
You are going to calculate it using calculus - and enjoy a sweet treat while your crunching those numbers!
In this activity, you will determine the rate of change of the volume of a Tootsie Roll Pop (TRP) as you consume it.
Equipment Needed:
• Tootsie Roll Pop (TRP)
• Graphing Calculator
• Ruler
Subject: A.P. Calculus
Unit: Related Rates
Process
Part 1
Step 1: Determine the initial radius of the TRP. (Assume it is a perfect sphere)
Step 2: Place it in your mouth and carefully suck for 30 seconds.
Step 3: Measure the radius and record the time and radius.
Step 4: Repeat steps 2 and 3 as many times as possible until you reach the chewy center.
Part 2
From your data, determine the rate of change of the radius of the TRP for your mouth power.
This may or may not be a constant rate.
Model both the radius using some type of regression and the rate of change of the radius.
Part 3
From your answer in part 2, you will graph 2 things:
•The volume of the TRP as a function of time.
•The rate of change of the volume over time.
Part 4
Finally, you will find your particular mouth sucking power by finding the average value of the rate of change of the volume of the TRP.
Evaluation
Altogether, you will hand in the following:
• the method you used to calculate the radius
• your data (time vs. radius)
• a graph of time vs. radius and the best fit equation. (TI graph links may be used to generate your graph. If you do not have one, use graph paper.)
• a graph of time vs. the change of the radius
• a graph of time vs. volume
• a graph of time vs. the change in volume
• your calculations for average value of the rate of the change of the volume of the TRP
Conclusion
Next time you see a speed limit for tootsie roll pop consuming, you will know if you're obeying the law!
Credits
Stu Schwartz