1. Using the graphs, explain why a logistic model makes sense for the data.

2. Referring to the data table, complete the following steps to create a logistic growth model in the form y = a/1+ be^-rx for the generation of wind in the state of Kansas.

a) According to the table, what is the initial value of the data and how can this information be translated to an ordered pair?

b) Based on the current resources, there is an estimated limit of 28,000 thousand megawatt hours. How does this fit into the standard form of the logistic model?

c) Using your answers from parts a and b above, solve for the value of b in the logistic function.

d) Use your results from above and the data point for 2017 to find the value of r in the logistic function.

e) Based on your above calculations, write a logistic equation that models the data.

f) Use the equation above to algebraically determine the estimated generated wind energy in the year

g) Explain how you could use a graphing tool to verify that your answer to the above problem is correct.

PART 2

1. Use a graphing tool and the data provided in the table in part 1 to write a logistic regression equation for the generation of wind in the state of Kansas.


2. Is the regression equation you found a good model for the data? Explain.


3. In Part 1, it was given that there is and estimated limit of 28,000 megawatt hours based on the current resources. How does this compare to the regression model and what could account for the difference?


4. Based on the logistic regression model, in what year did the generation of energy by wind transition from an increasing rate of change to a decreasing rate of change? Explain.

PART 3

1. Compare the model you wrote in part 1 with the regression model you found in part 2. which do you think is a better model? Explain.