Modelling using First Order Differential Equations (Edexcel A-Level Further Mathematics): Flashcards

$\frac{dP}{dt} = kP$

$P(t) = P_0 e^{kt}$

$\frac{dT}{dt} = -k(T - T_a)$

$T(t) = T_a + Ce^{-kt}$

$m\frac{dv}{dt} = mg - kv$

$v = \frac{mg}{k}$

$a = v\frac{dv}{ds}$

$F(x) = e^{\int P(x)dx}$

Exponential growth

Exponential decay