Growth & Decay Lab

Growth & Decay Lab 🧪

Money in a savings account, a car losing value, a population rising — all are **repeated percentage change**. Each period you apply the **same multiplier** again. This lab builds straight on the multiplier method: the trick is to raise the multiplier to a **power**. Goggles on.

Multipliers, again ✖️

Recall the multiplier for a percentage change: • **+5%** → × **1.05** • **−20%** → × **0.8** • **+100%** → × **2**. For repeated change over **n** periods, apply it **n times** — that is, raise it to the power n: **final = start × (multiplier)ⁿ**.

Match each change to its multiplier

Compound growth 📈

**Compound interest** adds interest, then earns interest on that interest. Each year multiply by the same multiplier: **£100 at 10% per year for 2 years** = 100 × 1.1 × 1.1 = 100 × 1.1² = **£121**. The power (²) is the number of years. For 3 years it would be 1.1³, and so on.

Compound interest

An interactive activity.

Order the method

An interactive activity.

Compound vs simple ⚖️

**Simple** interest adds the **same** amount each year (10% of the ORIGINAL): £100 → +£10 +£10 = **£120** after 2 years. **Compound** applies the percentage to the **new** balance each year, so year 2 earns a little more: **£121**. Compound always beats simple over time.

Which earns more?

£100 is saved for 2 years at 10% per year. Which earns MORE — simple interest or compound interest?

• Compound — it earns interest on the interest, giving £121 versus £120
• Simple — adding a fixed amount each year is more
• They earn exactly the same
• You cannot tell without the bank

Depreciation and decay 📉

Things that **lose** value work the same way, but the multiplier is **less than 1**. A car **depreciating 20% per year** uses × 0.8 each year: **£200 for 2 years** = 200 × 0.8² = 200 × 0.64 = **£128**.\n\nSame power rule, just a shrinking multiplier — the value decays instead of growing.

Depreciation

An interactive activity.

Growth and decay facts

Pick the TWO correct statements about repeated percentage change.

• Compound interest applies the percentage to the new (growing) amount each year
• A depreciation (decay) multiplier is less than 1
• Simple interest always earns more than compound interest
• You multiply by the multiplier only once, however many years pass

The lab rules

For repeated percentage change, raise the _____ to the power of the number of years. Compound interest beats simple interest because it applies the percentage to the _____ amount each year. A depreciation multiplier is _____ than 1.