Modelling with Exponentials & Logarithms (Edexcel A-Level Mathematics): Flashcards

Rate increases proportionally to current value.

$y = y_0 e^{kt}$ with $k > 0$.

Quantity decreases proportionally to current value.

$y = y_0 e^{-kt}$, where $k > 0$ for decay.

Doubling time = $\ln(2) / k$.

Half-life = $\ln(2) / k$.

Faster rates of growth or decay.

Population doubles over fixed time intervals.

$e$ is approximately $2.718$.

Radioactive decay and asset depreciation.