Modelling with first-order differential equations (HSC SSCE Mathematics Extension 1): Flashcards

It's written as y'(t) = f(t, y(t)), modeling changes.

Growth at a rate matching its current value, k > 0.

Written as y'(t) = ky(t) with k < 0.

Calculated as T = ln(2)/r.

Calculated as t_{1/2} = ln(2)/r.

y'(t) = f(t, y(t)), essential for modeling changes.

Use P'(t) = rP(t) and solve P(t) = P_0 e^{rt}.

Used in chemistry for reaction rates and pollutant spread.

Separation of variables is crucial for finding solutions.

To improve problem-solving skills and analysis.