1. Using the graphs, explain why a logistic model makes sense for the data. (4 points)

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? (2 points)

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? (2 points)
It fits in the model because it acts as the carrying capacity of the model

c) Using your answers from parts a and b above, solve for the value of b in the logistic function. (4 points)

d) Use your results from above and the data point for 2017 to find the value of r in the logistic function. (4 points)

e) Based on your above calculations, write the logistic equation that models the data. (2 points)

f) Use the equation above to algebraically determine the estimated generated wind energy in the year 2021 for Kansas. (2 points)

g) Explain how you could use a graphing tool to verify that your answer to the above problem is correct. (2 points)

Part 2: Find and apply a logistic regression model.

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. (8 points)

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

3. In Part 1, it was given that there is an estimated limit of 28,000 thousand megawatt hours based on the current resources. How does this compare to the regression model and what could account for the difference? (4 points)

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. (4 points)

Part 3: Justify and interpret logistic models.

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. (4 points)

2. Shown is a graph of net generation wind for Texas. The graph appears to take the shape of an exponential function. Would you recommend using a logistic function, like the model for Kansas, or an exponential function for this data? (3 points)

3. One logistic equation to model the California data is the equation found using regression. y = 21,430.4 1 + 7.27265 −0.160197 Which state, Kansas or California, had a greater number of years in which the growth of wind energy was increasing? Explain. (3 points)