Explanation Formula used: Equation of any logistic curve is y = L 1 + b e − k t . Proof: Consider the expression y = L 1 + b e − k t . To find the inflection point, find its first derivative and second derivative. It is known that the logistic differential equation is: d y d t = k y ( 1 − y L ) So, second derivative is: d 2 y d t 2 = d [ k y ( 1 − y L ) ] d t = d ( k y ) d t − d d t ( k y 2 L ) = k × d y d t − 2 k y L × d y d t Substitute d y d t = k y ( 1 − y L ) : d 2 y d t 2 = k × k y ( 1 − y L ) − 2 k y L × k y ( 1 − y L ) = k 2 y ( 1 − y L ) − 2 k 2

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ISBN: 9781337678445

Author: Larson, Edward

Publisher: CENGAGE L

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Chapter 6.4, Problem 31E

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To prove: The inflection point of any logistic curve is L2 when the solution starts below the carrying capacity L.

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Chapter 6.4, Problem 30E

Chapter 6.4, Problem 32E

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To prove: The inflection point of any logistic curve is L 2 when the solution starts below the carrying capacity L .

Solution Summary: The author explains that the inflection point of any logistic curve is L2 when the solution starts below the carrying capacity.

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To prove: The inflection point of any logistic curve is L2 when the solution starts below the carrying capacity L.

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