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Growth and Decay
   Problem 1.2 (complexity 2). Solution

A culture contains   bacteria, with the population increasing exponentially. The culture contains   bacteria after   hours. How long will it be until there are   bacteria?

Solution

First, we use the given information to evaluate the constant k .
 
 

Taking natural logarithms on both sides,
 
 
 
We must find the time when   .
 
 

Taking natural logarithms on both sides,
 
 
 

 Answer:  


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