Sample Calculus Lab: How Many Licks

Name:______Block:______

Objective: . To determine the rate of change of the volume of the tootsie roll lollipop at the time when the radius of the lollipop is three-fourths the original value.

Equipment Needed: • Tootsie Roll Pop/Blow Pop • Ruler  Timer (use the timer on your cell phone) • Graphing Calculator

Part 1 - Data Collection: Step 1: Determine the initial radius of the TRP/BP. (Assume it is a perfect sphere.) Step 2: Take the TRP/BP and suck on the lollipop for 30 seconds. Step 3: take out after every 30 second. Measure the radius with dental floss and record all your data into a table. Step 4: Repeat step 2 and 3 as many times as possible.

Time (s) Circumference C = 2πr (mm) Radius (mm) 0 30 60 90 120 150 180 210 240 270 Name:______Block:______

Part 2 - Data Analysis: Based on the data, determine the rate of change of the radius as a function Using the data from your table, graph the radius as a function of time on graph paper. From this graph determine the rate of change of the radius of the TRP/BP for your mouth power. Use a line of best fit to calculate the rate of change if data appears to be linear. Use the linear regression capabilities of your graphing calculator to find the best fit line. Name:______Block:______

Part 2: The Mission: Using these results and what you learned about related rates from Calculus class, determine how fast the volume of the TRP/BP is decreasing when the radius is three-fourths its original value. Be sure to include all calculus support and calculations. Show all work.

Part 4- Reflection Answer the following questions using complete sentences.

1. What happened to dr/dt as the radius decreased?

2. What happened to dV/dt as the radius decreased?

3. A well-known calculus text states that when sucked a TRP gives up volume at a rate of 0.8 cubic centimeters per minute. Based on your experiment, comment on the reasonableness of this value (percent error). How well did the theoretical dV/dt correlate with the actual dV/dt?

4. Discuss any assumptions made and/or any difficulties you had, that may contribute to the reasonableness.

5. Using the number of licks you counted in the first 30 seconds, calculate how many licks it does take to reach the center of a TRP.