# Modeling an Invasive Species Population

Examples, solutions, and videos to help Algebra I apply knowledge of exponential functions and transformations of functions to a contextual situation.

### New York State Common Core Math Algebra I, Module 3, Lesson 22

Lesson 22 Student Outcomes

Students apply knowledge of exponential functions and transformations of functions to a contextual situation.

Mathematical Modeling Exercise
The lionfish is a fish that is native to the western Pacific Ocean. The lionfish began appearing in the western Atlantic Ocean in 1985. This is probably because people bought them as pets and then dumped them in waterways leading to the ocean. Because it has no natural predators in this area, the number of lionfish grew very quickly and now has large populations throughout the Caribbean as well as along the eastern coastline of the United States and the Gulf of Mexico. Lionfish have recently been spotted as far north as New York and Rhode Island. The table below shows the number of new sightings by year reported to NAS (Nonindigenous Aquatic Species), which is a branch of the U.S. Geological Survey Department.

1. Complete the table by recording the total number of sightings for each year.
2. Examine the total number of sightings data. Which model appears to be a better fit for the data—linear or exponential? Explain your reasoning.
3. Make a scatter plot of the year versus the total number of sightings
4. Based on the scatter plot, either revise your answer from Exercise 2 or explain how the scatter plot supports your answer from Exercise 2.
5. On the scatter plot, draw a smooth curve that best fits the data.

Problem Set
Another Invasive Species Problem: Kudzu Kudzu, a perennial vine native to Southeast Asia, now covers a large area of the southern United States. Kudzu was promoted as a forage crop and an ornamental plant when it was introduced to the U.S. at the Philadelphia Centennial Exposition in 1876. Many southern farmers were encouraged to plant kudzu for erosion control from the mid-1930s to the mid-1950s. In 1953, kudzu was removed from the U.S. Department of Agriculture’s list of permissible cover plants due to its recognition as an invasive species. Look up information about kudzu in the U.S. on Wikipedia, and write a short (1- to 2-page) report on the growth of kudzu since its introduction. In your report, choose a function (linear or exponential) to model and graph the growth of kudzu (in hectares) in the U.S. per year over the past half century or so. Remember to cite your sources!

Lesson 22 Exit Ticket

1. For the equation found in Exercise 8, explain the parameters of the equation within the context of the problem.
2. Given each of the following, describe what features in the data or graph make it apparent that an exponential model would be more suitable than a linear model.
a. The table of data.
b. The scatterplot.
c. The average rates of change found in Exercise 6.
3. Use your equation from Exercise 8 to predict the number of lionfish sightings by year 2020. Is this prediction accurate? Explain.

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