Objective: To write an exponential model to fit a set of collected data.
Previous Knowledge: Students should have used the function f(x) = a(1 ± r)x to model exponential growth and decay.
Materials: 2 sided, 2 colored chips and Paper bag (optional)
Time: One 50 minute class period
Group Size: 2
Procedure: - Each group needs approximately 50 chips.
- Count the initial amount of chips and record the number in the chart below.
- Pick a color that will the one to be kept with each toss of the chips. (Example: If your chips are red on one side and yellow on the other and you decide to keep the yellow chips, every time you toss the chips you pick up the ones that land on the red side.)
- Drop the chips from the bag and pick up the appropriate colored chips and put them to the side. Count the remaining chips and record the number in the table below. Place the remaining chips back in the bag.
- Continue the process until 1 or zero chips of the chosen color remain.
| Number of Tosses | Number of Chips | Rate of Decrease
yn/(yn - 1) | | 0 | | | | 1 | | | | 2 | | | | 3 | | | | 4 | | | | 5 | | | | 6 | | |
- Using graph paper, make a graph pf the data. (Make sure each axis is labeled and the units are numbered appropriately.)
- In the third column of the chart, find the rate of decrease (yn/yn – 1) between the data points.
- Write the equation of the function that best fits the data.
- Enter the data into your graphing calculator, graph your equation, and see how closely it fits your points.
- The graph of your function is continuous, while the graph of your data is discrete. Which graph is the appropriate one for the situation?
- If the function you wrote represents the radioactive decay of the Gulliksen7 isotope (with a half-life of one year), and you started with the same number of grams of Gulliksen7 as you did chips, find the amount of time it would take the isotope to decay to 18 grams.
- How much Gulliksen7 would you have after 3 ½ years? After 4 years and 4 months?
- If the Gulliksen7 isotope had a half life of 6 months rather than 1 year, how long would it take the isotope to decay to 18 grams?
- If the Gulliksen7 isotope had a half life of 3 months, how much Gulliksen7 would you have after 1 ½ years?
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