Answer
15 years
Work Step by Step
grow from 400 ducks to 1000 ducks
growth rate of 6.2% per year
$1000=400*(1.062)^x$
$1000/400=400*(1.062)^x/400$
$2.5 =(1.062)^x$
$log 2.5 = x log 1.062$
$log 2.5/log 1.062 = x log 1.062/log 1.062$
$x = 15.232$
15 years