3.7. Logistic Functions http://www.ck12.org
3.7 Logistic Functions
Here you will explore the graph and equation of the logistic function.
Exponential growth increases without bound. This is reasonable for some situations; however, for populations there
is usually some type of upper bound. This can be caused by limitations on food, space or other scarce resources. The
effect of this limiting upper bound is a curve that grows exponentially at first and then slows down and hardly grows
at all. What are some other situations in which logistic growth would be an appropriate model?
Watch This
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URL: http://www.ck12.org/flx/render/embeddedobject/61004http://www.youtube.com/watch?v=OSMPeY354cU Finding a Logistic Function
Guidance
The logistic equation is of the form:f(x) = 1 +ca·bx
The lettersa,bandcare constants that can be changed to match the situation being modeled. The constantcis
particularly important because it is the limit to growth. This is also known as the carrying capacity.
The following logistic function has a carrying capacity of 2 which can be directly observed from its graph.
f(x) = 1 +^20. 1 x
An important note about the logistic function is that it has an inflection point. From the previous graph you can
observe that at the point (0, 1) the graph transitions from curving up (concave up) to curving down (concave