Nonlinearmodels

6.3.4 Journal: Nonlinear Models Journal Algebra 1B Name: _______________________ Points Possible: 20 Date: _______________________ Scenario: Rabbit Population In 1859, an Australian had 24 rabbits shipped to Australia. Within 70 years, there were an estimated 10 billion rabbits in Australia. A hypothetical rabbit population is shown in the table below. Your Task Your goal is to create models to represent the growth of the population. Using the data in the table below, answer the questions, showing your work for all calculations. Here is the data for the hypothetical (or imagined) rabbit population. Year (x) 0 1 2 3 4 5 6 7 8 9 Number of rabbits (y) 6 8 1 2 1 6 2 3 3 2 4 5 6 3 8 8 12 4 1. Looking at the data, does this rabbit growth appear linear, exponential, or quadratic? Explain your answer. ( 1 point ) 2. Make a scatterplot for the data. You can either create your scatterplot on paper and insert a photo or create it using www.desmos.com/calculator and insert a screenshot. Desmos instructions are listed below. ( 2 points )  Choose the “+” symbol from the upper left hand corner.  Choose “table”.  In the table, type the year values from the table above under “x” and the rabbit population values under “y”.  Screenshot your scatterplot and insert the photo below.

3. Looking at the scatterplot you created, which regression model (linear, exponential, or quadratic) do you think best fits the data? Explain your answer. ( 1 point ) 4. Use a graphing calculator or www.desmos.com/calculator to calculate a quadratic regression. Write the equation below. This video contains an example of how to use desmos to calculate a quadratic regression: https://youtu.be/cer_oSOgdlY . ( 2 points ) 5. Use the equation from #4 to predict the population of the rabbits in year 70. Show your work. ( 2 points: 1 point for showing work, 1 point for the population ) 6. Compare your quadratic model to an exponential model by calculating an exponential regression, using either a graphing calculator or www.desmos.com/calculator . Write the equation below. This video contains an example of how to use desmos to find an exponential regression: https://youtu.be/O-hx7i3TkEg ( 2 points )

b. How does your answer to part (a) compare with your guess about the model in question #1? ( 1 point ) 10. The video says there were an estimated 10 billion rabbits in Australia after 70 years. Which of your predictions (the quadratic model prediction in question #5 or the exponential model prediction in question #7) was closer to this estimate? ( 1 point ) Read these two articles on populations: Wildlife Journal- Population and National Geographic-Rabbits . What are some factors that could impact the population growth of the rabbits? List at least three. ( 3 points )