Applications
The differential equation representing exponential growth is
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About This Question
- 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 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).
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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