Posted: September 16th, 2017

Exponential functions & models

Iris has been studying “aninvasive population of snails. This particular snail has no local

predators so the population grows wildly. She has observed that the population follows an

exponential rate of growth for fifteen years.

1. Create your own exponential function, f(x), which models the snail population. You will

need to identify the principal population of the snails and the rate of growth each year.

Explain to Iris how your function shows the principal population and the rate of growth,

in complete sentences.

2. A local snail population grows according to the function g(x) = 200(1.03?x. Demonstrate

the steps to convert g(x) into an equivalent function with only x as the exponent. Then

explain to Iris how the key features of this local snail population compares to the key

features of the invasive population.

3. Iris wants to graph the invasive snail population to show the city council. Justify what the

appropriate domain and range would be for the function f(x), what the y-intercept would

be, and if the function is increasing or decreasing.

4. In five years, a garden festival plans on using the park where Iris has been studying the

invasive snails. Explain to the garden festival committee how to find the average rate of

change for the snail population between years 2 and 5. Describe what this average rate of

change represents.