Part a
Assuming the bacterial growth is modeled by the separable differential equation \(\frac{dy}{dt} = ay(b-y)\), use the data points (1, 2.3) and (4, 13.5) to estimate the constants \(a\) and \(b\). Outline your method by forming equations using these points and provide the resulting approximate parameter estimates.
Modeling Chemical Reaction Kinetics Using a Separable Differential Equation
A laboratory experiment involves a chemical reaction where the concentration \(C(t)\) of a reactant changes over time according to the model \(\frac{dC}{dt} = k(C_0 – C)\). A student uses Euler’s method to approximate \(C(t)\) at discrete time intervals for parameter fitting purposes. Suppose that at time \(t=0\), the concentration is \(C(0)=0\) and \(C_0\) represents the […]