6.5 Growth, decay and repeated percentage change — Learn

Prerequisites: percentage multipliers, powers and reverse percentages.

Objectives: model repeated percentage growth and decay, and interpret the multiplier.

For repeated growth, use $1+r/100$ as the multiplier. For decay, use $1-r/100$. Raise the multiplier to the number of equal time periods, then multiply by the starting value.

Example 1. A population of 2,000 grows by 3% each year for four years.

The multiplier is 1.03.

After four years, $2000 × 1.03^4 = 2251.01762$.

To the nearest person, the population is 2,251.

Example 2. A machine worth £8,000 loses 12% of its value each year for three years.

The remaining-value multiplier is 0.88.

After three years, $8000 × 0.88^3 = 5449.216$.

To the nearest penny, its value is £5,449.22.

Watch out. A 12% decrease uses 0.88, not 0.12. Check that a decay model gives a value below the starting value.

You should now be able to

• select a growth or decay multiplier;
• raise the multiplier to the number of periods;
• interpret and round a repeated-change result.