Differential Equations for Engineers · Linear systems, eigenstructure, and matrix exponentials
A colony initially contains 800 bacteria and grows at a rate proportional to the square…
Problem
A colony initially contains \(800\) bacteria and grows at a rate proportional to the square root of its population. After \(6\) hours the population is \(1250\). Formulate and solve an initial-value problem for the population, and determine when it reaches \(2450\).
Hint
The model is \(P'=k\sqrt{P}\) with \(P(0)=800\); separate variables.
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