Flip one sign and growth becomes decay: $A = A_0(1 - r)^t$, read aloud A equals A-nought, times one minus r, to the t. Accountants write the same law with their own letters — $B = C(1 - d)^k$, the declining-balance book value of an asset that cost $C$ new and is written down $d$ of its remaining value each year. Same machine, different stationery.

The named trap of this lesson is adding where you should subtract. A car that loses 20% a year is multiplied by 0.80, not 1.20 — and if your answer is bigger than the sticker price, the sign slipped. The second trap is subtler and worth a moment: $1 - rt$ is straight-line depreciation, the same dollars off every year, and it hits zero eventually. $(1 - r)^t$ takes a percent of a shrinking balance, so it approaches zero without ever arriving. That is why a fifteen-year-old car is still worth something, and why the two methods give different numbers on the same asset.

One more nugget worth carrying: losing 20% then gaining 20% does not bring you home. $100 \to 80 \to 96$. Percentages are not symmetric, because the second one is charged on a different base.