SOLUTION: Please help!!! The half life of an element is 3.9 * 10^9 yr. How long does it take a sample of the element to decay to 2/5 of its original mass? Use A=A0(1/2)^(t/T) where AO is

Question 576524: Please help!!!
The half life of an element is 3.9 * 10^9 yr. How long does it take a sample of the element to decay to 2/5 of its original mass? Use A=A0(1/2)^(t/T) where AO is the initial amount, T is the half life, and t is the time. (express results in scientific notation, rounded to the nearest hundredth)

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
is the equation given and you want the value of that will make
(You know it has to be more than because at T you would have 1/2 left and 2/5<1/2).
We could divide both sides by to get

Taking logarithm of both sides
--> --> --> -->
Plugging in the values given,

Using the approximate values for the logarithms

So,

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