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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.

Calculus: Early Transcendentals
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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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.
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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