Answer:
The plant was alive for 1155 years
Explanation:
Any radioactive decay process follows the exponential law which is mathematically expressed as:
\(N(t)= N(0)e^{-kt}------(1)\)
where N(0) = initial amount of the radioactive material
N(t) = amount at time t
k = decay constant
The decay constant is in turn related to the half-life t1/2
\(k = \frac{0.693}{t1/2}----(2)\)
It is given that t1/2 of 14C = 5730yrs. Therefore:
\(k = \frac{0.693}{5730}=1.21*10^{-4}yr-1\)
In addition it is mentioned that:
N(t) = 1/4*N(0)
substituting this in equation (1) gives:
\(1/4*N(0)= N(0)e^{-1.21*10^{-4}t}\)
t = 1155 years
