imo class 12 differential equations

The population of a city grows at a rate equal to 5% of its current population per year. The differential equation for population P at time t is:

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The population of a city grows at a rate equal to 5% of its current population per year. The differential equation for population P at time t is:

  • A. dP/dt = 5P
  • B. dP/dt = 0.5P
  • C. dP/dt = 0.05P
  • D. dP/dt = P/5

Answer: C) dP/dt = 0.05P

Explanation: Rate of growth dP/dt = 5% of P = (5/100)P = 0.05P.

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