Exponential Growth

N(t) = N_0 e^{rt}

Population doubles repeatedly at a constant proportional rate.

By Thomas Malthus, Various

Biological Sciences

Exponential Growth

1798 · Thomas Malthus

Why it matters: Simplest growth model—basis for bacteria, viruses, and compound interest analogies.

Discoverers: Thomas Malthus, Various (1798)

What does it mean?

Population doubles repeatedly at a constant proportional rate.

Simplest growth model—basis for bacteria, viruses, and compound interest analogies.

Symbol	Name	Unit	Meaning
$N₀$	Initial population	—	Starting count
$r$	Growth rate	—	Per capita growth rate
$t$	Time	—	Elapsed time

r=0.1/hr → doubling time ≈ 6.9 hours.

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Equation Universe

N(t) = N_0 e^{rt}

Real-world impact

Wireless technology

Electromagnetic waves carry information worldwide.

Photo: Unsplash — network infrastructure

Population doubles repeatedly at a constant proportional rate.

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