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Percentage growth

If a quantity grows by the same percentage each period, you multiply by the same growth factor every time. The growth factor is 1 plus the percentage as a decimal. The starting value is multiplied by the growth factor raised to the number of periods. The model is used for population, prices and interest when the percentage stays fixed. A fixed amount of money per year is linear, not exponential.

Try it yourself

Exponential growth

f(x) = a \cdot b^x

exponential model

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

growth factor

Symbols

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

Example

20,000 inhabitants and 2% growth per year. After 5 years: $20\,000 \cdot 1.02^5 \approx 22\,081.6$ .

For a decrease of p percent the growth factor is 1 minus p/100.

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Part of Mathematics S1: Functions and models.