Beaver Island is a beautiful place located in Lake Michigan. The island has become overrun with beavers so the Wildlife Federation of Michigan released coyotes on the island to stabilize the beaver population. In 2018, the population of beavers was 24,576 and began to decrease at a rate of 2.5% per year. In the same year, the population of coyotes was at 16,786 and was increasing at a rate of 1.8% per year. Assume that there is no outside factor and that these rates continue in order to answer the following questions.

1. Create a table of values for each population. Find AND analyze the first-differences. What can you say about the population-growth/decay?

2. Create an exponential function that describes the Beaver population AND create an exponential function that describes the Coyote population. How did you come up with this equation?

3. On the same graph, plot the function that represents the beaver population AND the function that represents the Coyote population.

4. How do the populations differ? How are they related?

5. When would the population of coyotes be greater than the population of beavers?

6. When would the populations be the same? How can you tell?

7. What will happen to both the beaver and coyote populations if this trend continues?

8. Write a brief paragraph summarizing your findings regarding the beaver and coyote populations.