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Question

The differential equation representing exponential growth is

RankGuru · Accepted Answer

1. **Core Concept**: Exponential growth occurs when the rate of change of a quantity is directly proportional to the current amount of the quantity.
2. **Translation**: 'Rate of change' is $\frac{dy}{dt}$. 'Proportional to $y$' is $ky$.
3. **Formula**: $\frac{dy}{dt} = ky$.
4. **Solution Extension**: Solving this gives $y(t) = y_0 e^{kt}$. This models populations, compound interest, and radioactive decay (for $k < 0$).

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