Exponential (Leaving Cert Mathematics): Revision Notes

Exponential

Exponential functions are in the form :

where :

• $a$ is the initial value ($y$-intercept when $x=0$)
• $b$ is the base of the exponential function
  • If $b>1$, the graph represents exponential growth.
  • If $0<b<1$, the graph represents exponential decay.
• $x$ is an independent variable.

$0.5(3)^x$

$0.5(0.1)^x$

Characteristics

• The graph always passes through $(0,a)$, since $b^0=1$.
• In exponential decay, the graph decreases rapidly as $x$ increases but never actually reaches zero.