Logistic Models
Student Guide
Assignment Summary
For this assignment, you will use a logistic model to represent real-world data and will justify and interpret
the model in the context of a given scenario.
Background Information
Many real-world phenomena show exponential growth for a period of time, but that growth is limited by
resources such as food and space. The limiting resource causes the growth to slow and reach a limiting
value. These types of situations are best modeled by logistic functions. One such example is the
generation of energy. States use many ways of generating energy such as wind, water, and solar panels.
Some forms of generating energy may be better suited for some states than others. Natural resources
such as the amount of sunlight, wind, water, or land play an important factor in how energy is generated
in a given state. If land is available, windmills can be constructed to generate energy by wind. However,
having a large number of windmills will not guarantee more energy because the region may not get much
wind to turn the windmills.
Assignment Instructions
For this project, you are expected to submit the assignment.
Step 1: Prepare for the performance task.
a) Read through the guide before you begin so you know the expectations for this assignment.
b) If there is anything that is not clear to you, be sure to ask your teacher.
c) If your word processing program has an equation editor, you can insert your equations here.
Otherwise, print this activity sheet and write your answers by hand.
Step 2: Complete Parts 1, 2, and 3 in the Assignment section of this document.
a) Read all directions carefully.
b) Complete each task.
c) Insert images or screenshots of graphs when needed. Be sure that all graphs or screenshots
include appropriate information such as titles, labeled axes, etc.
d) Be sure to show all your work. You will be given partial credit based on the work you show and
the completeness and accuracy of your explanations.
e) Consider underlining and circling important components in the problems.
Step 3: Evaluate your project using this checklist.
If you can check each box below, you are ready to submit your project.
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Have you answered all questions in Parts 1, 2, and 3?
Have you shown your work?
Did you include an image or screenshot of a graph when requested?
Are all your equations correct? Be sure to check your formatting carefully.
Step 4: Revise and submit your project.
a) If you were unable to check off all of the requirements on the checklist, go back and make
sure that your project is complete. Save your project before submitting it.
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Student Guide (continued)
b) Your teacher will give you further directions about how to submit your work. You may be
asked to submit your responses through the Virtual Classroom, email it to your teacher, or
print it and hand in a hard copy.
c) Congratulations! You have completed your project.
Assignment
Part 1: Write and apply a logistic model for a data set.
The US Energy Information Administration collects data recording the net generation of energy by wind
annually, in thousands of megawatt hours for each state. The graphs show the data for Kansas and
California, respectively. Some of the data points in these graphs are given in the table.
"Wind Energy in Kansas." Wind Exchange. Accessed September 25, 2019.
https://windexchange.energy.gov/states/ks.
"Wind Energy in California." Wind Exchange. Accessed September 25, 2019.
https://windexchange.energy.gov/states/ca.
Net Generation for Wind (in Thousands of Megawatts)
Year
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Kansas
California
2001
40
3,500
2002
467
3,803
2003
366
3,895
2004
359
4,306
2005
426
4,262
2006
992
4,883
2007
1,153
5,585
2008
1,759
5,385
2009
2,863
5,840
2010
3,405
6,079
2011
3,720
7,752
2012
5,195
9,754
Student Guide (continued)
2013
9,433
12,822
2014
10,845
12,992
2015
10,999
12,230
2016
14,111
13,509
2017
18,598
12,823
2018
19,295
13,650
"Electricity Data Browser." U.S. Energy Information Administration.
https://www.eia.gov/electricity/data/browser/#/topic/0?agg=1,0,2&fuel=008&geo=vvvvvvvvvvvvo&sec=o3g&linech
art=ELEC.GEN.WND-KS-99.A~~&columnchart=ELEC.GEN.WND-US-99.A~ELEC.GEN.WND-IA99.A~ELEC.GEN.WND-.
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
a
y=
-rx for the generation of wind in the state of Kansas.
1 + be
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)
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)
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Student Guide (continued)
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)
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Student Guide (continued)
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)
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Student Guide (continued)
"Wind Energy in Texas." Wind Exchange. Accessed September 25, 2019. https://windexchange.energy.gov/states/tx.
3. One logistic equation to model the California data is the equation found using regression.
y=
21,430.4
1 + 7.27265𝑒 −0.160197𝑥
Which state, Kansas or California, had a greater number of years in which the growth of wind energy was
increasing? Explain. (3 points)
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