Algebra
Intermediate

Exponential Growth / Decay

Growth (k>0) or decay (k<0) over time.

Formula

A=A0ektA = A_0 e^{kt}

Variables

A_0Initial amount
kRate
tTime

Example

A colony of 100 bacteria growing at k = 0.5/h reaches 100·e^(0.5·3) ≈ 448 after 3 hours.

Did You Know?

Exponential growth is deceptively slow at first then explosive — the reason compound interest and pandemics surprise people.

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