Too Many People, or Not Enough?

Today my Precalculus students did an activity that models population growth. I used an activity developed by Scott Danielson that I modified slightly for my own use. You can download his original documentation here.

Students start with some beans in a “Bean Pot”, 10 beans in a “Parents” cup, and an empty “Children’s Cup”. They flip two pennies. If two heads, do nothing. If two tails, a member of the population has died, so take a bean from the Parents cup, and put it in the Bean Pot. If one head, one tail, a child has been born, so take a bean from the Parents cup and one from the Bean Pot, and put them in the Childrens cup. Repeat the coin tossing until there are no more Parents beans. This counts as one generation. Count the beans in the Childrens cup, and put them in the Parents cup to start a new generation.

After a few generations, the girls started getting nice exponential growth. It took them about 45 minutes to do 8 generations, so that’s as far as we went. By entering the generations and the population at each generation into their graphing calculators, they were able to get an exponential model  for their data, and make some predictions of future populations.

After some discussion to make sure everyone’s data was reasonable, and everyone understood what the exponential function was giving them, we then watched the two short videos below:

All in all, a fairly successful lesson, and they left feeling optimistic about their future :).

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