The half-life of cobalt-60 is 5.3 years. What fraction of a sample remains after 21.2 years?

A) one half
B) one quarter (WRONG)
C) one eighth (WRONG)
D) one sixteenth

please explain!!!

one sixteenth

Explanation: Since we know the half life of Cobalt-60 is 5.3 years, and 21.2 years have passed, we can determine how many half lifes have passed by doing division:

21.2 / 5.3 = 4

Since four half lifes have passed, we need to set up the following:

1 / 2^4 (always raise the two to the number of half lifes that have passed, in this case, four have passed, which is what we determined up above!)

When you simplify this you get 1 / 16, which is answer D.

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