Exponential Growth and Decay • Topic 1 of 4

Growth Models

A quantity that grows by a fixed percentage each period follows A = P(1 + r)^t, where P is the starting amount, r the growth rate as a decimal, and t the number of periods. A base (1 + r) greater than 1 signals growth. For 500 growing 20% per period, after 2 periods it is 500(1.2)² = 500 × 1.44 = 720. Convert the percent to a decimal, add 1, raise to the number of periods, and multiply by the start. The exponent counts periods, not years unless stated. The SAT keeps the exponent small so the arithmetic is exact and tests whether you set up (1 + r)^t correctly.

Exponential growth curve rising from a low start and curving upward ever more steeplyExponential growthPtimeamountA = P(1 + r) to the power t → grows faster each period

✅ Solved examples

1. 500 grows 20% per period. Value after 2 periods?
500(1.2)² = 500 × 1.44 = 720.
2. 200 grows 10% per period. Value after 2 periods?
200(1.1)² = 242.
3. 100 grows 50% per period. Value after 2 periods?
100(1.5)² = 225.
4. Does A = 300(1.2)^t describe growth or decay?
Base 1.2 > 1, so growth.

✏️ Practice — try these, take hints as needed

1. 400 grows 10% per period. Value after 2 periods?
400(1.1)².
400 × 1.21.
—
484.
2. 600 grows 20% per period. Value after 2 periods?
600 × 1.44.
—
—
864.
3. 200 grows 50% per period. Value after 2 periods?
200 × 2.25.
—
—
450.
4. 1,000 grows 10% per period. Value after 2 periods?
1000 × 1.21.
—
—
1,210.
5. Does A = 250(1.05)^t describe growth or decay?
Base > 1?
—
—
Growth.

📝 Topic test — 8 questions

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Decay Models →