Bunnies! (Exponential Growth & Decay Functions)
Description of student activity:
Students will see an application of exponential growth and decay though modeling the population of bunnies. Growth when they are multiplying and decay when (sadly) a pack of hungry wolves finds our happy (imaginary) bunnies. Students will also complete exercises for transformations of the exponential functions.
To start this activity, students (or the teacher) will read the introductory page to the lesson that discusses what an exponential function is as well as the backstory to our model. The backstory consists of real facts about bunnies as well as discussing what assumptions will be made for our model.
Next, the students will complete a table for months 11 through 14 of the bunny population as well as calculate the population ratio increase from month to month. These ratios will be averaged to estimate the common ratio used in the model that they will write. Lastly, they will use the model to calculate the bunny population at 3 years as well as plot points on the pre-graphed model to discuss its accuracy.
They will then create a model for the bunny’s exponential decay after wolves discover them. Creating this model will include a horizontal shift of 36 units to the right.
Lastly, students will be given examples of all four transformations (Vertical Shift, Horizontal Shift, Vertical Compression, and Vertical Stretch) that they will use to graph 3 equations. Two of the graphs will also illustrate that a vertical stretch can be an identical transformation to a horizontal shift for exponential functions and students will be asked to explain why.
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