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Exponential functions

An exponential function describes growth or decline by the same percentage in each period. The initial value $a$ is multiplied by the growth factor $b$ once per period. If $b > 1$ there is growth, and if $0 < b < 1$ there is decline. The growth factor for an increase of $p$ percent is $1 + p/100$ .

Try it yourself

The linear function

f(x) = a\cdot b^x

exponential function

b = 1 + \frac{p}{100}

growth factor

Symbols

$a$	initial value
$b$	growth factor
$p$	percent per period	%

Example

5000 kr is deposited at 4% interest per year. After 10 years: $5000\cdot 1.04^{10} \approx 7401$ kr.

For a decline of

p

percent the growth factor is

1 - p/100

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Part of Mathematics 1T: Functions.