Have students shake up the bag and drop the pennies on the ground. Any penny showing tails represents an animal that has died and should be removed. In a table, students should record the number of remaining pennies and then place them back in the bag. They should repeat this process five times, representing five years in the life of the cohort's existence. Have the students graph the data in the table and discuss what they notice about the population changes over time.
Older students can use a graphing calculator to fit a function to the data.
Discuss with students the possible limitations of this mathematical model. Each year, the population size is one-half of the previous year. With calculators, students can model the population changes by entering 100 and then multiplying the answer by 0.5 repeatedly to view predicted populations over time. Again, a calculator can be used to predict cohort populations. Students should realize that both functions have limits of 0, but in a finite time, the functions never take on their limiting value.