Explanation Given information: The statement “The logistic function P = L ( 1 + C e − k t ) approaches L as t increase.” For positive constants L, C, and k, a logistic function has the form P = f ( t ) = L 1 + C e − k t . The parameter L of the logistic function is the value at which P levels off, where P = L 1 + C e − k t . This value L is called the carrying capacity and represents the largest population an environment can support.One way to estimate the carrying capacity is to find the inflection point. The graph of a logistic curve is concave up at first and then concave down. At the inflection point, where the concavity changes, the slope is largest. To the left of this point, the graph is concave up and the rate of growthis increasing. To the right of this point, the graph is concave down and the rate of growth is diminishing.The inflection point is called the point of diminishing returns. Properties of the logistic function P = L 1 + C e − k t The limiting value L represents the carrying capacity for P

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Chapter 4, Problem 65SYU

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Chapter 4, Problem 64SYU

Chapter 4, Problem 66SYU

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Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

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To indicate: Whether the statement is true or false.

Solution Summary: The author explains that a logistic function has the form P=L(1+Ce-kt). The limiting value L represents the carrying capacity for P.

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Chapter 4 Solutions

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