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Growth factor

The growth factor is the number you multiply by once per period. An increase of $p$ percent gives the factor $1 + p/100$ , and a decrease gives $1 - p/100$ . The factor is greater than 1 for growth and between 0 and 1 for decline. If you read off a model $a\cdot b^x$ , the percentage is $(b - 1)\cdot 100$ . A linear model adds the same number each time. An exponential model multiplies by the same factor.

Try it yourself

Exponential growth

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

increase

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

decrease

f(x) = a\cdot b^x

the model

Symbols

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

Example

A decrease of 7% gives $b = 1 - 0.07 = 0.93$ . An increase of 12% gives $b = 1.12$ . $f(x) = 200\cdot 1.1^x$ gives $f(2) = 200\cdot 1.21 = 242$ .

A decrease of 7% is the factor 0.93, not

-0.07

Practise exponential models for free →

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Part of Mathematics 1T: Exponential models.