Modeling with Logistic Growth Functions
Internet Users (per 100 people) in the U.S. vs. Time
1.) What type of model best suits the data in the graph above? ________
The data used to create the graph above was obtained from
www.gapminder.org and is provided in the table below:
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Internet Users (per 100 people)
in the U.S.
0.78
1.16
1.72
2.27
4.87
9.27
16.51
21.78
30.39
36.26
43.64
49.76
59.63
62.61
65.73
69
70
72.5
74.1
Modeling with Logistic Growth Functions
1.) Graph a scatter plot of the data on your graphing calculator. Let t=0
represent the year 1990.
2.) Find the logistic model for the data that gives P as a function of t on
your graphing calculator and record your model below:
3.) Graph your model by using the following short cut:
4.) Use your model to predict the number of Internet users (per 100
people) in the U.S. in 2011. __________________
5.) In what year was the number of Internet subscribers growing the
fastest? ____________________
6.) What are the asymptotes for your model? _________________
7.) What is the carrying capacity based on the model? __________
What do you think about this number ? ___________________
________________________________________________
________________________________________________
________________________________________________
Modeling with Logistic Growth Functions
Suppose the table below shows the population of an endangered species
released into a game preserve through 14 months. Use a graphing calculator
to find a logistic growth model that gives P as a function of t.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
t 0
P 100 114 132 156 180 225 281 349 390 453 502 542 568 597 620
1.) Graph a scatter plot of the data. What type of model best suits the
data in the table above ? ___________________
2.) Find the logistic model for the data that gives P as a function of t on
your graphing calculator and record your model below:
3.) Graph your model by using the following short cut:
4.) Use your model to predict the population of the endangered species in
the game preserve after 15 months.
5.) In what month was the number endangered species growing the
fastest in the game preserve?
6.) What are the asymptotes for your model? _________________
7.) What is the carrying capacity based on the model? __________
Explain this number _________________________________
________________________________________________
Modeling with Logistic Growth Functions