EXAMPLE 4 Logistic population growth Assume 50 fruit flies are in a large jar at the beginning of an experiment. Let P(t) be the number of fruit flies in the jar t days later. At first, the population grows exponentially, but due to limited space and food supply, the growth rate decreases and the population is prevented from growing without bound. This experiment is modeled by the logistic equation – 0.10(1 - P ,for t > 0, 300, dP dt together with the initial condition P(0) = 50. Solve this initial value problem.
EXAMPLE 4 Logistic population growth Assume 50 fruit flies are in a large jar at the beginning of an experiment. Let P(t) be the number of fruit flies in the jar t days later. At first, the population grows exponentially, but due to limited space and food supply, the growth rate decreases and the population is prevented from growing without bound. This experiment is modeled by the logistic equation – 0.10(1 - P ,for t > 0, 300, dP dt together with the initial condition P(0) = 50. Solve this initial value problem.
Chapter5: Exponential And Logarithmic Functions
Section5.5: Exponential And Logarithmic Models
Problem 30E: The table shows the mid-year populations (in millions) of five countries in 2015 and the projected...
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Transcribed Image Text:EXAMPLE 4 Logistic population growth Assume 50 fruit flies are in a large jar at the
beginning of an experiment. Let P(t) be the number of fruit flies in the jar t days later. At
first, the population grows exponentially, but due to limited space and food supply, the
growth rate decreases and the population is prevented from growing without bound. This
experiment is modeled by the logistic equation
– 0.10(1 -
P
,for t > 0,
300,
dP
dt
together with the initial condition P(0) = 50. Solve this initial value problem.
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