Radium-221 has a half-life of 30 seconds. How long will it take for 85% of a sample to decay?

Ok so I really don't know what to do here. I know I can find r because its but what about the 85%? Any help is appreciated.

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- October 2nd 2008, 12:15 PMn8thatsmeHalf-life
Radium-221 has a half-life of 30 seconds. How long will it take for 85% of a sample to decay?

Ok so I really don't know what to do here. I know I can find r because its but what about the 85%? Any help is appreciated. - October 2nd 2008, 12:24 PMChris L T521
Let be the initial amount of Radium-221, and let be the current amount of Radium.

Since 85% decayed, that means that the current amount is 15% of the original amount.

Thus, this implies that

Since the decay is modeled by , we see now that

Now, k can be found using the half-life formula: , where is the half-life.

So our equation now has the form

Can you take it from here?

--Chris