All courses › Foundations of Mathematics › Exponential function

Exponential function

An exponential function $f(x)=a\cdot b^x$ multiplies by the same factor $b$ for every increase of $x$ by 1, unlike a linear function which adds the same amount. In physics and calculus the base $e$ is often used.

f(x) = a\cdot b^x

exponential function,

a=f(0)

N(t) = N_0 e^{kt}

with the natural base e

Symbols

$a,\ N_0$	initial value
$b$	growth factor per step
$k$	growth rate ( $k>0$ growth, $k<0$ decay)	1/time

Example

$N_0=200$ , 5% growth per year: $N(3)=200\cdot 1.05^3 \approx 231.5$ .

10% growth two years in a row gives

1.1^2=1.21

, i.e. 21%, not 20%.

Practise exponential and logarithmic functions for free →

← Zeros and discriminant · Logarithms →

Part of Foundations of Mathematics: Exponential and logarithmic functions.