Diff-EQ: At time t=0, James was given unknown amount of unknown radioactive substance

blakesHue

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At time t=0, James was given an unknown amount of unknown radioactive substance & was told to take measurements in milligram of that radioactive substance at time t1,t2 and t3 which are measured in days .

Hence 0<t1<t2<t3.

James recorded the amount a, b and c respectively at t1,t2,t3.

It is known that t1,t2,t3 forms a arithmetic progression.

It is also known that (a*c)=3000

Assuming James lost his result of amount b a few days after the whole experiment, how does he manage to find it back using just calculations?

Hi, I need help with the above question. Was wondering that if we do not know the starting amount & half life of the unknown substance, how do I go about calculating b.
 
Hi, I need help with the above question. Was wondering that if we do not know the starting amount & half life of the unknown substance, how do I go about calculating b.
At time t=0, James was given an unknown amount of unknown radioactive substance & was told to take measurements in milligram of that radioactive substance at time t1,t2and t3 which are measured in days .

Hence 0<t1<t2<t3.

James recorded the amount a, b and c respectively at t1,t2,t3.

It is known that t1,t2,t3 forms a arithmetic progression.

It is also known that (a*c)=3000

Assuming James lost his result of amount b a few days after the whole experiment, how does he manage to find it back using just calculations?

Do you know the equation to be used for radio-active decay?
 
Hi, I need help with the above question. Was wondering that if we do not know the starting amount & half life of the unknown substance, how do I go about calculating b.

I see what you did there, no worries, here are some hints.

Hint 0: Dont worry about the many unknown variables :D

Hint 1: Remember anything taught in your lectures or tutorials about radioactive decay?

Hint 2: What can you derive from the fact that the three timings are arithmetic progression?

Hint 3: Play around with some simplification tricks and you will see better

Cheers!
 
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