Applications of Logistic Growth Models
Cell phone (per 100 people) in the U.S. vs. Time
Note: The data in the graph above is from www.gapminder.org
The number of cell phone subscribers has grown exponentially over the past
10 years; however, in developed countries, the market has become saturated.
Let t = the number of years since 1997. Let C(t) represent the number of
cell phone subscribers t years since 1997 in developed countries.
C(t) =
100
1+ 5.93e"0.39t
1.) Asymptotes: _____________________
2.) The number of cell phone subscribers is limited to
______________ per 100 people. This number is
referred to as the ___________________ .
!
3.) In what year was the number of cell phone subscribers growing the
fastest?
Applications of Logistic Growth Models
A conservation organization releases some animals of an endangered species
into a game preserve. The organization believes endangered species
population P will be modeled by:
P(t) =
1000
1+ 9e"0.1656t
where t is the time measured in months.
1.) Find the initial number animals released into the game preserve_____
!
2.) What will the endangered species population be after 8 months?
_________
3.) Asymptotes: _____________________
4.) The population reaches its maximum growth rate at: __________
5.) The population is limited to ______________. This number is
referred to as the ___________________ .
Applications of Logistic Growth Models