Repeated change multiplies.

A fixed percentage change multiplies the current value each time. A 6% increase uses multiplier 1.06; a 6% decrease uses 0.94. After n equal periods, multiply by the same factor n times.

A fixed dollar change is linear, while a fixed percentage change is exponential. State the initial amount, the period and the assumption that the rate remains constant. Real savings or depreciation may include fees or changing rates outside the simple model.

INTERACTIVE MODEL

Try it. Watch it change.

y =

3.2^{x}

+ 0

Base control (r shown above)1 Vertical shift k0Input x1

f(1) = 3.2 · asymptote y = 0

The graph is calculated from the displayed rule. Drag the highlighted point or use the sliders.

Explore: Switch from a base above 1 to a base below 1. Compare growth and decay on the same axes.

Compound growth

A_n=A_0(1+r)^n

WORKED EXAMPLE

A $500 device loses 20% of its value each year. Model its value after three years.

V(n) = 500(0.8)ⁿ.
V(3) = 500 × 0.512 = $256.

Assumed knowledge

Percentages, decimals and powers.

Learning checkpoints & source

YOUR LEARNING CHECKPOINT

Model repeated percentage growth and decay.
Distinguish exponential change from linear change.

Year 10 preparation ↗

READY TO TRY IT?

Repeated change multiplies.

A $500 device loses 20% of its value each year. Model its value after three years.

Put the idea to work.