Exponential Functions (Leaving Cert Mathematics): Flashcards

$f(x) = a \times b^x$

Initial value (value when $x = 0$)

Base

$b > 1$

$0 < b < 1$

All real numbers ($x \in \mathbb{R}$)

Positive real numbers ($f(x) > 0$)

$x$-axis or $y = 0$

$(0, a)$

$\int e^x \, dx = e^x + C$

$\frac{a}{\ln(b)} \times b^x + C$ where $b > 0$, $b \neq 1$

Population growth, radioactive decay, compound interest

Curves upwards

Curves downwards