A certain radioactive isotope has a half-life of 5 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?

Question

anonymous · Answer

what does this question even asking for? how do I approach it? im confused

anonymous · Answer

hey just in case I don't reply in the next few minutes I just wanted to let you know I have to pee and then find a calculator:P

parthkohli · Answer

OK. Again, this question lists a very complicated application of geometric sequences: radioactivity. 

Suppose that I have a radioactive substance with me. This radioactive thing is pretty unstable. So what it does is release some of its mass as radiations. And if you keep observing it in regular intervals of time, you'll see that it has become lighter. So it loses its mass.

The half-life of a radioactive substance is the time a sample of that substance takes to reduce itself to half of its mass. So if the half-life is 1 second, and I have 2 grams of a sample, then after 1 second I will observe that the radioactive substance has only 1 grams. After two seconds, it will have 0.5 grams, and after three, 0.25 grams.

parthkohli · Answer

So you see - the mass is a geometric sequence with common ratio 1/2!

anonymous · Answer

ahh ok I see. but then would it make the first column an arithmetic sequence and the second column negative then? lol im really more confused on what the question is asking than I am with the actual math right now

parthkohli · Answer

Do you have a picture of the table?

parthkohli · Answer

Oh wait, we don't need one.

parthkohli · Answer

Column-1 Time                          Column-2 Mass
t = 0                                                  32 g
t = 5 days                                          32/2 = 16 g
t = 10 days                                        16/2 = 8 g
t = 15 days                                        8/2 = 4 g
t = 20 days                                        4/2 = 2 g
t = 25 days                                        2/2 = 1 g

anonymous · Answer

ok so would the answer be that the time is an arithmetic sequence that increases by 5 and the mass is a geometric sequence with a common ratio of 1/2?

parthkohli · Answer

Indeed.

anonymous · Answer

ok then thanks so much for all your help:) you rock!

parthkohli · Answer

Thanks!