Time to fill the cup

This can be done by GP.

First we have 2 bacteria from 1, Then from the 2 we get 4, Again from the 4 we get 8, and so on,

So Series is 2,4,8,16,......

Now $t_n= 2. 2^{n-1}$ [nth Term of the GP]

So at t=30 minutes

$t_{30} = 2. 2^{29}$

So Now for another $t_{30}$ we can say that $2.t{30}$ , Because at $t_{30}$ half was filled again the next half will be filled when 2 times

Hence Full cup = $2. t_{30}$ = $2. 2^{30}$ = $t_{31}$ .

So $\boxed{31 \text{minutes}}$ is the answer.

Since it already filled half of the cup, it needs to divide into 2 once more to fill the whole cup which takes one minute.
30+1=31

this is a trick problem, so you really have to think about it. There is NO knowledge of exponents needed in this. JUST LOGIC.

Ok, so given that it doubles every minute, and that at 30 minutes it is at half, it must double the next minute and become a WHOLE. Therefore, the bacteria will become whole the next minute, which is 31 minutes.