Carbon dating mathematical modelling
When translated into a self-consistent set of differential equations, the model becomes a mathematical model, a quantitative version of the hypothesis. However, the next step is to reduce the mathematical model to a computable form; anatomically and physiologically realistic models account of the spatial gradients in concentrations within blood-tissue exchange units, while compartmental models simplify the equations by using the average concentrations.
The former are known as distributed models and the latter as lumped compartmental or mixing chamber models.
This question can be answered using a little bit of calculus. Once we have an expression for t, a "definite integral" will give us the mean value of t (this is how "mean value" is defined).
From the equation above, taking logarithms of both sides we see that lt = -ln(N/N.
The raw 'uncalibrated' radiocarbon ages are given in radiocarbon years before the present day (BP) but these do not equate directly to actual calendar years due to variations in atmospheric carbon over time.