Explanation Given: The logistic model is, d p d t = ( a − b p ) p ; p ( t 0 ) = p 0 Approach: The equilibrium solution is given by d x d t = 0 . Calculation: The logistic model is given as, d p d t = ( a − b p ) p … ( 1 ) Solve the equation ( 1 ) as, ∫ d p ( a − b p ) p = ∫ d t ∫ [ 1 a p + b a ( a − b p ) ] d p = ∫ d t 1 a ln p − 1 a ln ( a − b p ) = t + C Further solve, 1 a [ ln ( p ( a − b p ) ) ] = t + C ln ( p ( a − b p ) ) = a t + C a p ( a − b p ) = e a t + C a p = a e a t + C a − b p e a t + C a Further solve,

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Chapter 3.2, Problem 11E

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Any solution to the given logistic model approaches equilibrium solution p(t)≡a/b as t approaches +∞.

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Chapter 3.2, Problem 10E

Chapter 3.2, Problem 12E

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Any solution to the given logistic model approaches equilibrium solution p ( t ) ≡ a / b as t approaches + ∞ .

Solution Summary: The author explains that any solution to the given logistic model approaches equilibrium solution p(t)equiv a/b as +infty .

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Any solution to the given logistic model approaches equilibrium solution p(t)≡a/b as t approaches +∞.

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Any solution to the given logistic model approaches equilibrium solution p ( t ) ≡ a / b as t approaches + ∞ .

Solution Summary: The author explains that any solution to the given logistic model approaches equilibrium solution p(t)equiv a/b as +infty .

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To show: Any solution to the given logistic model approaches equilibrium solution p(t)≡a/b as t approaches +∞.

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Chapter 3 Solutions

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Any solution to the given logistic model approaches equilibrium solution p(t)≡a/b as t approaches +∞.