Write a differential equation to model the situation given. Do not solve.
Tests of an artifact discovered at the Debert site in Nova Scotia show that 28% of the original 14C is still present. What is the probable age of the artifact?
To model the situation given, we can use a differential equation that represents the decay of the 14C isotope over time. The decay of a radioactive substance typically follows an exponential decay model.
Let's denote the amount of 14C at any given time t as Q(t). The rate of decay of 14C is proportional to the amount of 14C present at that time, which means the differential equation can be written as:
dQ/dt = -k * Q(t),
where k is the decay constant.
Given that 28% of the original 14C is still present, we can assume that Q(0) = 1 (the original amount of 14C). Thus, at t = 0, the differential equation becomes:
dQ/dt = -k.
Now, we can solve this differential equation to find Q(t) and determine the probable age of the artifact by finding the value of t such that Q(t) = 0.28 (28% of the original 14C).