Applications
The differential equation representing exponential growth is
Select the correct option:
Solution
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 dtdy. 'Proportional to y' is ky.
- Formula: dtdy=ky.
- Solution Extension: Solving this gives y(t)=y0ekt. This models populations, compound interest, and radioactive decay (for k<0).
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About This Question
- Subject
- mathematics
- Chapter
- differential equations
- Topic
- applications
- Difficulty
- Easy
- Year
- 2025
This easy difficulty mathematics question is from the chapter differential equations, covering the topic of applications. It appeared in the 2025 exam. Practice this and similar questions to strengthen your understanding of differential equations concepts.
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