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Exponential decrease

If a quantity falls by the same percentage each period, the growth factor is less than 1 and greater than 0. A ten percent decrease gives the growth factor 0.9, not minus 0.1. You multiply the starting value by this factor once per period. The value becomes smaller, but the formula alone does not make it negative. A fixed amount subtracted each period is linear decrease, not exponential.

Try it yourself

Exponential growth

f(n) = a \cdot b^n

decrease when 0 < b < 1

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

growth factor for a decrease

Symbols

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

Example

An item worth 500 NOK loses 10% of its value each year.

After 5 years: $500 \cdot 0.9^5 \approx 295.25$ NOK.

A ten percent decrease is the factor 0.9. Do not subtract 10% of the starting value five times.

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← Growth by a fixed percentage · Finding the growth factor →

Part of Mathematics S1: Exponential models.