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The differential equation representing exponential growth is

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dy/dt = ky

dy/dt = k

dy/dt = kt

dy/dt = k/y

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Subject: mathematics
Chapter: differential equations
Topic: applications
Difficulty: Easy
Year: 2025

Solution

Correct Answer:

dy/dt = ky

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

This easy difficulty mathematics question is from the chapter differential equations, covering the topic of applications. It appeared in the 2025 exam.

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