Question 1089081: The function A = A^ down 0e^-0.01386x models the amount in pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since the material was put into the vault. If 400 pounds of the material are initially put into the vault, how many pounds will be left after 120 years?
Answer by ikleyn(52790)   (Show Source):
You can put this solution on YOUR website! .
When I see the problems similar to this, coming to the forum, it becomes clear to me that the people do not know
and do not understand correctly what the radioactive decay is.
The radioactive decay is the process of transforming of material's nuclei to other nuclei with emitting radiation,
light particles (neutrino), sometimes neutrons.
You can read about it from Wikipedia, for example.
https://en.wikipedia.org/wiki/Radioactive_decay
The mass (the part) of emitted radiation or light particle is negligibly small.
The total mass of the material in container practically does not change.
Simply one sort of atoms transforms to others, but the total mass remains practically the same.
Had the total mass significantly changed at the process, it would be an atomic explosion (like A-bomb), not a radioactive decay.
What is true, that the mass of selected material at the radioactive decay transforms to other materials according
to the given formulas, but the total mass remains practically unchanged, or is changed to very small portion.
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So, the formulas and the values given in this post, relate to the PARTICULAR material, but not to the total mass in the closed container.
Thus instead of solving the problem I read some lecture in Physics (on radioactive decay) for you.
I think it is justified, otherwise you never will learn it.
I am sure that other tutors will come and will show you how to solve this problem quantitatively.
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