Answer:
Differential equation:
,
,
,
.
Solution:

Explanation:
Let suppose that rate of change of the amount of Carbon-14 atoms are directly proportional to the current amount of Carbon-14 atoms. That is:


Where:
- Amount of Carbon-14 atoms, dimensionless.
- Proportionality constant, measured in
.
must be negative as death rate is constant and birth rate is zero. (
). Dimensionally, we can rewritte this constant as following:

Where
is the time constant (
), measured in years.
We can find the solution of the ordinary differential equation by separating each variable:






Where
is the initial amount of atoms of Carbon-14.