Scientists who do carbon 14 dating use 5700 years for its half life. find the age of a sample in which 10% of the radioactive nuclei originally present have decayed

For this problem, we use the formula for radioactive decay which is expressed as follows:

An = Ao (e^-kt)

where An is the amount left after time t, Ao is the initial amount and k is a constant determined experimentally. 
First, we calculate for the value of k from the data we have of the half life. We do as follows:

An = Ao (e^-kt)
0.5 = e^-k(5700)
k = 1.21x10^-4 / year

After solving for k, we can use this value to solve for the age of the sample given the percent of the carbon nuclei that is remained after that particular time,

An = Ao (e^-kt)

An/Ao = e^-kt
1 - .10 = e^-1.21x10^-4(t)
t = 878.00 years

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