You need to know that because it follows first order kinetics, the half-life is constant. If only forty percent remains after one hour, then you know that the half life is less than one hour (100 --> 50 should take less time than going from 100 -->40, which takes one hour). This narrows down your answers to A,B, or C. A is too much of a difference, so the answer choice should be either B or C. Someone else want to try?

First order mean's it's constant. That means in X min, amount decreases by half.
It can't be A, because if it was 30 min, 1 hour would be two half lives so it would be at 25%.
If it's C, then at the 50 min mark, there's 50 % left. In another 10 min, 1/5 of amount would have decreased ( if its constant ), so you'd be left with 80% (4/5) of the amount that's left at the 50 min mark (50% left).
80% of 50% is 48%.

That means you'd have 48% of original amount left. So it has to be B.
EDIT: 80% of 50% is 40%. My bad. It's C
Hope that helps. I know the second paragraph can get confusing.

If 30 min, then there would be 25% after one hour.
If 46 min, then there would be 50% after 46 min, 25% after 1 hour 32 min, so about 40% after one hour.
If 50 min, then there would be 50% after 50 min, 25% after 1 hour 40 min, so about 45% after one hour.
If 64 min, then there would be over 50% after one hour.

This is a TBR question, right? I remember not liking their solution as much as mine.

Here's the general equation for exponential decay half-life (from the definition):

N(t)=N(0)(1/2)^t/t1/2, where N(0)=initial quantity at t=0, N(t)=quantity remaining at time t, and t1/2=the "half life."

So, N(0)=1, t=1 hour, and N(t)=0.4 and 0.4=1x(1/2)^1/t1/2. Taking ln of both sides and simplifying yields: t1/2=ln0.5/ln0.4=0.7565hours, or 45.3882 minutes, which means 46 minutes is the closest answer.

Of course you could guesstimate this answer without using a calculator, as previously described.

At the first half-life you have 50% of the original. In this case you only have 40%.

So if you setup a ratio: 50/40 = 1.25, you can use that ratio to find out how much time would pass for X amount to be remaining for any half-life you want.

This method really only works since there are only 4 possible answers (actually 2 since you can easily rule out 30min and 60min). It's a guess and check type of thing.

So anyway, if the half-life is 46 minutes, 46*1.25 = 57.5 Same for if the half-life is 50minutes. 50*1.25 = 62.5 or whatever I said earlier.

At the first half-life you have 50% of the original. In this case you only have 40%.

So if you setup a ratio: 50/40 = 1.25, you can use that ratio to find out how much time would pass for X amount to be remaining for any half-life you want.

This method really only works since there are only 4 possible answers (actually 2 since you can easily rule out 30min and 60min). It's a guess and check type of thing.

So anyway, if the half-life is 46 minutes, 46*1.25 = 57.5 Same for if the half-life is 50minutes. 50*1.25 = 62.5 or whatever I said earlier.