6.3.4 journal: nonlinear models

scenario: rabbit population

show your work for all calculations.
here are the data for the hypothetical (or imagined) rabbit population.

year (x) 0 1 2 3 4 5 6 7 8 9 10
number of rabbits (y) 6 8 10 14 19 25 33 43 57 77 104

1. looking at the data, does this rabbit growth look linear, quadratic, or exponential? explain your answer.
(1 point)

2. make a scatterplot for the data. (2 points)

3. looking at the scatterplot, which regression model do you think fits the data? explain your answer.
(1 point)

4. using a graphing calculator, find the quadratic regression equation for the rabbit data.
(2 points: 1 point for identifying constants, 1 for the equation)

5. using the quadratic regression equation from question 4, predict the number of rabbits in year 70.
(2 points: 1 point for setting up the correct equation, 1 for simplifying)

6. using a graphing calculator, find the exponential regression equation for the rabbit data.
(2 points: 1 point for identifying the constants, 1 for the equation)

7. using the exponential regression equation from question 6, predict the number of rabbits in year 70.
(2 points: 1 point for setting up the correct equation, 1 for simplifying)

8. compare the predicted number of rabbits for year 70 using the quadratic model (question 5) with the predicted number using the exponential model (question 7). which prediction is larger? (1 point)

9. is it reasonable to use this data set to predict the hypothetical number of rabbits for year 70? explain.
(1 point)

making a decision

10. these graphs show the scatterplot with the quadratic regression equation and the exponential regression equation.
a) which do you think is a better fit? why? (2 points: 1 point for choice, 1 point for explanation)

b) how does your answer to part (a) compare with your guess about the best model in question 1? was your initial choice correct? (1 point)

analyze your results

11. the video says there were an estimated 10 billion rabbits in australia after 70 years.
a) how does your predicted number of rabbits for the hypothetical population compare with the actual rabbit population in australia in year 70? (1 point)

b) why do you think the rabbit population in australia can grow so large? (1 point)

c) what are some factors that might prevent a rabbit population from growing infinitely large? (1 point)