Answer:
1859 years
Step-by-step explanation:
The equation that gives the general decay of a radioactive isotope is:
[tex]A(t) = A_0 e^{-\lambda t}[/tex]
where
A0 is the initial amount of the isotope at time t = 0
A(t) is the amount of the isotope at time t
[tex]\lambda[/tex] is the decay constant of the isotope
For the carbon-14 isotope we have the equation:
[tex]A(t) = 25e^{-0.00012t}[/tex]
Which means that
A0 = 25 g is the initial amount of carbon-14
[tex]\lambda = 0.00012 y^{-1}[/tex] is the decay constant
We want to find the time t after which the amount of substance left is
A(t) = 20 g
So, by re-arranging the equation for t, we find:
[tex] t = -\frac{ln(A(t)/25)}{0.00012}=1859 y[/tex]
