Ravi bought a bike for ₹80,000. Its value depreciates at a rate proportional to its current value. Which differential equation represents this situation (V = value, t = time)?

Ravi bought a bike for ₹80,000. Its value depreciates at a rate proportional to its current value. Which differential equation represents this situation (V = value, t = time)?

• A. dV/dt = kV
• B. dV/dt = −kV
• C. dV/dt = k/V
• D. dV/dt = k − V

Answer: B) dV/dt = −kV

Explanation: Depreciation implies a decrease over time, so the rate of change is negative and proportional to the value V. Hence, dV/dt = −kV (where k > 0).