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The amount of time that it takes a population to triple if the growth rate is 3.9%:

 

Use the compound interest formula:  A  =  Pe^r·t

A  =  final amount         P  =  initial amount          r  =  rate (as a decimal)         t  =  time

--->   Let the initial amount = x, then the final amount will be 3x         r  =  0.039         time = t

--->     3x  =  x·e^0.039·t  

Divide both sides by x:

--->     3  =  e^0.039·t  

Take the ln of both sides:

--->     ln(3)  =  ln( e^0.039·t )

Using the appropriate property of logs:

--->     ln(3)  =  0.039 · t · ln( e )

Since the ln(e)  =  1:

--->     ln(3)  =  0.039·t

Divide both sides by 0.039:

--->     t  =  ln(3) / 0.039  =  28.17 years (approximately)  or  28 years, 2 months

 #1 geno3141 has calculated the population using 3.9% compounded continuously. However, the question says the " annual growth rate is 3.9%", which implies "annual compound", since the compounding period is not explicitly stated. Based on this, we can calculate the number of years slightly differently:

FP=PP (1.039)^N: FP=Future population, PP=Present population.

3=1(1.039)^N take the Log of both sides

N=Log(3) / Log(1.039)

N=28.72, or about 28 years and 9 months