For a start, if the question does say "find the number of years", there is no need to round. It is not asking for a whole number of years.
The exception is if something is increasing on a specific date every year. But then it is not exponential growth because the growth is not continuous - it is like compound interest.
The answer is that if you must attain a certain number (ie. being close is not good enough, you must reach or exceed the number) then you round up.
If being as close as possible is the aim (whether slightly below or slightly above), then round off.
But in the HSC, they won't penalise for failing to round, unless it is specifically asked for, or implied by the wording. And there will only ever be a maximum of one mark in the entire paper that they allocate for rounding.
