math

An element has a half-life of 30 years. If 1.0 mg of this element decays over a period of 90 years, how many mg of this element would remain?
Begin amount is 1.0
elapsed time is 90y half life 30 years
n=9/30 n=3
90/2^2
90/8 = 11.25mg
thinking it's wrong not sure what I missed.

A 2.5 gram sample of a radioactive element was formed in a 1960 explosion of an atomic bomb at Johnson Island in the Pacific Test Site. The half-life of the radioactive element is 28 years. How much of this element will remain after 112 years?

I tried it this way 112/28= 4 half lives then 2.5/3 1.25
1.25/2=0.625
06.25/2= 0.3125
0.3125/2=0.15625 gram

which is the correct way to do these problems. Am I doing that the correct way

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  1. 90 years is 3 half-lives. That means that 1/8 of the original amount remains. So, the 1 mg that has decayed represents 7/8 of the original amount. So, starting out at 8/7 g, 1/7 g = 14.27mg remains.

    ----------------------------------

    after 4 half-lives, 1/16 of the original amount remains.

    2.5/16 = 0.15625g
    you are correct

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