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The growth of a new restaurant depends on the number of its regular customers as p'(t) = .01₁√√p(t) where p (t) represents the number of regular customers at any time t and p'(t) represents the rate at which the number of regular customers is changing at any time t. Solve this differential equation subject to the condition that p = 81 when t = 0. p(t)

The growth of a new restaurant depends on the number of its regular customers as p'(t) = .01₁√√p(t) where p (t) represents the number of regular customers at any time t and p'(t) represents the rate at which the number of regular customers is changing at any time t. Solve this differential equation subject to the condition that p = 81 when t = 0. p(t)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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The growth of a new restaurant depends on the number of its regular customers as p'(t) = .01√/p(t) where p (t) represents the number of regular customers at any time t and p'(t) represents the rate at which the number of regular customers is changing at any time t. Solve this differential equation 81 when t = 0. subject to the condition that p p(t)
Transcribed Image Text:The growth of a new restaurant depends on the number of its regular customers as p'(t) = .01√/p(t) where p (t) represents the number of regular customers at any time t and p'(t) represents the rate at which the number of regular customers is changing at any time t. Solve this differential equation 81 when t = 0. subject to the condition that p p(t)
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