Growth of bacteria diff. eq help

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mayeh
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a bacterial population B is known to have a rate of growth proportional to B itself. if between noon and 2 PM the population triples, at what time, no controls exerted should B become 100 times what it was at noon?


what does it mean by between noon and 2pm? does it mean that it takes 2hrs for the bacteria to triple? or the bacteria triples from 12 to the middle of 12 and 2?
 
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F(1400 hours) = 3 x F(noon).
 
sorry, i don't get it...

could you please explain further.
 
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Population at 1400 hours (2 PM) = 3 times the population at noon.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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