The question I have been given is:
A population of bacteria in a petri dish grows in such a way that after every passing of a minute, the number of bacteria in the population doubles. Assume there was 1 bacterium to start with. How many will there be after 24 hours assuming none of the bacteria dies and that the available nutrients for the bacteria in the petri dish were unlimited.
To calculate this I have used this method of compound interest I have used this formula.
$o$ = OriginalValue
$i$ = interestRate
$t$ = total increments
$o \cdot i^t$
$1 \cdot 2^{60 \cdot 24} = 1 \cdot 2^{1440}$
To get this answer:
$3.0422419887462074119071134929958\times 10^{433}$
but others think the formula should be $o \cdot 2^{t-1}$ thus $1 \cdot 2^{1439}$
$1.5211209943731037059535567464979\times 10^{433}$
which is correct?
"After" 24 hours would mean after the last minute that makes up the 24 hours, so I think that you are correct.
I suspect the "others" might be using a geometric sequence to model the growth and think that they are looking for the value of the $1440$th term, which would be $2^{1439}$, but that wouldn't be correct. If we do want to use a geometric sequence to model the growth and we want term 1 to map to the population after minute 1, term 2, after minute 2, etc, then notice that the first term is no longer one bacterium, but two (i.e. the population after one minute). In that case, the term associated with the population after the last minute would be $2\cdot2^{1439}$, which is the same as your answer.