## AAMC Sec 1 QB #60

Snazia
Posts: 9
Joined: Fri Mar 09, 2018 9:57 pm

### AAMC Sec 1 QB #60

This question is asking for how much samble is left if the hlaf-life is 4500 days and the sample was left for 13,500 days. The answer is 1/8, but I can't see why 3 half lifes would have passed. Wouldn't half the sample be left 4500 days, 1/4 after 9000 days, and 1/8 after 18000. Wouldn't there have to be more than 1/8 at 13500. Can someone explain where I'm going wrong?I have attached the relevant parts of the question.

pi.png
pi.png
Attachments
pi1.png
NS_Tutor_Andrew
Posts: 520
Joined: Mon May 23, 2016 1:47 pm

### Re: AAMC Sec 1 QB #60

Hi Snazia,

The idea here is that half-life intervals are obtained as follows: If the half-life time is n days, the first half-life will take place in n days, the second one in 2n (or n+n days), the third one in 3n (or 2n + n) days, the fourth one in 4n (or 3n + n) days, etc. So if it was 4 days, the sequence of half-life intervals would be 4, 8, 12, 16, 20 days, etc.

Therefore, you're right that the first half-life in this case would pass in 4500 days and the second one would pass in 9000 days. Then, the third one will be at 3*4500 or 9000+4500 days (=13,500 days). It looks like the obtain 18,000, you multiplied the second half-life interval (9000 days) by 2, when instead, you need either 3x the half-life or the second half-life interval + the half-life itself.

Hope this helps clarify this question! If not, I'd suggest writing it out with some sample half-life times.
Andrew D.
Content Manager, Next Step Test Prep.
Snazia
Posts: 9
Joined: Fri Mar 09, 2018 9:57 pm

### Re: AAMC Sec 1 QB #60

Ah, I see. I'm not sure why I doubled the time like that. Thank you!
NS_Tutor_Andrew