# A bacteria doubles its population in 8 hours. At this rate how many hours would it take the population of the bacteria to triple?

##### 1 Answer

Time taken for 3 times the population to have grown is:

12 hours 40 minutes and say 47 seconds

#### Explanation:

Let the rate of growth be constant and of value

Let time in hours be

Let count of bacteria at any time

So initial count of bacteria would be

Given that count of bacteria after 8 hours (

Required to determine unknown time

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The increase in bacteria after 1 hour is

The increase in bacteria after 2 hour is

The increase in bacteria after 2 hour is

So after 8 hours we have:

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Using equation(1) divide both sides by

Taking roots

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Using Equation(1) we have:

But

Taking logs ( I elect to use log to base 10 )

But

My calculator gives:

Is there could be a degree of error in the calculation lets say: