Let be the original amount of the substance and be the current amount of the substance.

Now, radioactive decay takes on the form , where is the decay constant. We need to know what is, because the half life of this substance is defined by , where is the half life.

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The first bit of information gives us enough info to find k.

It takes a year for the substance to decay to 95.5% of the original amount.

Thus, we see that , where we replaced with .

This now simplifies to

Now we can find the half life:

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Now, can you find , such that ?? [this was what the second part of the question was asking for]

Does this make sense?

--Chris