Using Exps & Logs in Modelling (Edexcel A-Level Mathematics): Flashcards

Variable appears in the power, e.g., $y = 3^x$.

$P$ represents population in the equation.

$P$ approaches $0$ as $t$ increases.

Take $\ln(P) = \ln(A) - kt$.

$y = \ln(P)$, $x = t$ in the linear form.

$R = kT^n$ describes the orbit radius and period.

$\ln(R) = \ln(k) + n \ln(T)$ for linear plotting.

Plotting $\ln(R)$ against $\ln(T)$ should yield a straight line.

$n = \Delta y / \Delta x$ from plotted values.

$R = 1.89 \times 10^{5} \times T^{0.697}$.