An Example ofFitting ODE Parameters to Data

Using ExcelNarrated by

Kerry Braxton-AndrewAnd

Josh Katzenstein

Modeling Radioactive Decay Rates

• Model EquationdN/dt = −λ * N(t)

• Decay Constant — λ — the inverse of the average lifetime of any given particle

• Number of Particles — N(t) — the total number of particles at a given time.

The Setup in Excel• Tabulate your experimental data

In this case time (t) and amount remaining (N)• Numerically determine dN/dt• Using the model equation guess a value for the

decay constant λ and determine dN/dt• Calculate the square of the residuals between

the dN/dt values for each time t• Sum the square of the residuals• Goal seek to minimize sum of square residuals

Based experimental data on research from the following source: http://www.eas.asu.edu/~holbert/eee460/RadioactiveDecay.pdf