Each time you dumped the pennies, one half-life passed; it has been shown that the half-life for this radioactive isotope is 20 years
in the year 2000, an archaeology team unearths pottery and is using this isotope for radiometric dating to place the age of the pottery
it is shown that 95% of the nuclei have decayed
approximately how long ago was the pottery made?

The exponential decay function is shown as:

At = Ao*2^(-t/h)

Where:

At = Final amount
Ao = original amount
t = time
h = years for half-life to occur

We are not given the original and final amounts, but we are told that after the certain amount of time had passed, only 5% had remained. So if we were to isolate At and Ao in one side of the equation, such that: At/Ao = 0.05, we can solve for the missing variable, which is t.

Substituting:

At/Ao = 2^(-t/h)
0.05 = 2^(-t/20)
t = 86.44 years

Therefore, the pottery was made approximately 86.44 years ago.

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