Logistic Functions and the Carrying Capacity of the Earth The function with M, A, k all positive, is known as a logistic function (Figure 4). Such functions are used to model phenomena that have an initial rapid increase but then level M P(t) = 1+Ae-kt » P off toward some finite value. From 1950 to 1980 to 2010 the human population of the earth grew from 2.65 to 4.45 to 6.90 billion people. Let t represent time in years since 1950 and P represent the population in billions. Using the (t, P) values for 1950, 1980, and 2010, and employing a computer algebra system to solve for M, A, and k in P(t), we obtain the logistic world- population model: M 17.4 P(t) = 1+ 5.56e-0.022t FIGURE 4 The logistic function M P(t) = 1+ Ae¬kt · Find lim P(t). t00
Logistic Functions and the Carrying Capacity of the Earth The function with M, A, k all positive, is known as a logistic function (Figure 4). Such functions are used to model phenomena that have an initial rapid increase but then level M P(t) = 1+Ae-kt » P off toward some finite value. From 1950 to 1980 to 2010 the human population of the earth grew from 2.65 to 4.45 to 6.90 billion people. Let t represent time in years since 1950 and P represent the population in billions. Using the (t, P) values for 1950, 1980, and 2010, and employing a computer algebra system to solve for M, A, and k in P(t), we obtain the logistic world- population model: M 17.4 P(t) = 1+ 5.56e-0.022t FIGURE 4 The logistic function M P(t) = 1+ Ae¬kt · Find lim P(t). t00
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Logistic Functions and the Carrying Capacity of the Earth The function
with M, A, k all positive, is known as a logistic function (Figure 4). Such
functions are used to model phenomena that have an initial rapid increase but then level
M
P(t) =
1+Ae-kt »
P
off toward some finite value.
From 1950 to 1980 to 2010 the human population of the earth grew from 2.65 to
4.45 to 6.90 billion people. Let t represent time in years since 1950 and P represent the
population in billions. Using the (t, P) values for 1950, 1980, and 2010, and employing
a computer algebra system to solve for M, A, and k in P(t), we obtain the logistic world-
population model:
M
17.4
P(t) =
1+ 5.56e-0.022t
FIGURE 4 The logistic function
M
P(t) = 1+ Ae¬kt ·
Find lim P(t).
t00
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