In Unit 6: Modeling Exponential Growth, there is a supplemental problem around Observing a Mouse Population (p.143). The problem looks at a group of scientists that are studying the mouse population on an island for a period of ten years. The scientists determine that they can use the following function to calculate the population of mice on the island after a given time:

f(t) = 120(1.08)^t

Question 4 of that activity asks students to graph the population for years 1 through 10 of the study. Students are then asked what they notice about the shape of the graph.

Elena Diamond, a teacher at York College, noticed that this section of the graph appears almost linear and doesn’t resemble what we expect when we think of the graph of an exponential growth function. We don’t want students to have the sense that the graph of exponential growth is linear and it might be worthwhile to tease out why it appears like it is here.

The .docx link above contains two graphs.

• The first is the graph of the function from -5 to 15, which will look similar to what students create. We played with the increments in both axes so students will have to use some graph reading skills to find the 10 year/260 mice point.
• Show your students the second graph after the first and ask them what they notice. The second graph resembles what we think of when we think of a graph of exponential growth. It does this by looking at a longer period of time, which is something you want students to discuss.
  • You may also want to ask them questions about the negative side (such as “What does -40 or -60 years mean in the context of this situation?”).
  • You might also ask them to compare the growth of the rabbit population overall to the growth of the population during the scientific study mentioned in the problem.

 

How else can we use these graphs?