Need math help with a continuous exponential growth model.

Mathematics
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The number of bacteria in a certain population increases according to a Continuous exponential growth model, with a growth rate parameter of 1.1% per hour. how many hours does it take for the size of the sample to double?

Note: this is a continuous exponential growth model.

Do not round any immediate computation, and round your answer to the nearest hundredth.

Dec 9th, 2015

Thank you for the opportunity to help you with your question!

The exponential model is  N = N(0) e^kt

Here we need to find the time for the population to double,  which means  N = 2 N(0)  and the rate k = 1.1% = 0.011

2 N(0)  = N(0) e^ 0.011 t

Dividing both sides by N(0), we have  2 = e^0.011t

Taking natural logarithm both sides, we have

ln(2)  =  ln (e^0.011t)

ln(2)  =  0.011 t

t = ln(2) / 0.011  =  63 hours. 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Dec 9th, 2015

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