Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the number present at any time. If there are no bacteria present at t = 0, how many are there at a later time? Observe here that the routine separation of variables solution gives an unreasonable answer, and the correct answer, N ≡ 0, is not obtainable from the routine solution. (You have to think, not just follow rules!)
Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the number present at any time. If there are no bacteria present at t = 0, how many are there at a later time? Observe here that the routine separation of variables solution gives an unreasonable answer, and the correct answer, N ≡ 0, is not obtainable from the routine solution. (You have to think, not just follow rules!)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 64E
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Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the number present at any time. If there are no bacteria present at t = 0, how many are there at a later time? Observe here that the routine separation of variables solution gives an unreasonable answer, and the correct answer, N ≡ 0, is not obtainable from the routine solution. (You have to think, not just follow rules!)
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