All courses › Mathematics 2P › Growth by a fixed percentage

Growth by a fixed percentage

If something grows by the same percentage each period, the model is exponential. The starting value is multiplied by the growth factor once per period. Two percent growth gives the factor 1.02, not 2. A fixed increase in the number of people per year is linear, not exponential. After many periods the exponential model becomes much larger than the linear one, even if they start equal. The rounding below is to the nearest whole inhabitant.

f(x) = a \cdot b^x

exponential model

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

growth factor

Symbols

$a$	starting value
$p$	percent per period	%

Example

20,000 inhabitants and 2% growth per year. After 10 years: $20\,000 \cdot 1.02^{10} \approx 24\,380$ .

A fixed percentage gives an exponential model. A fixed amount gives a linear one.

Practise exponential growth for free →

← Quartiles · Half-life →

Part of Mathematics 2P: Exponential growth.