Answer:
Differential equation: , , , .
Solution:
Step-by-step 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.