Iris has been studying an invasive 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.
- 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.
- A local snail population grows according to the function g(x) = 200(1.03)2x. 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.
- 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.
- 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.