imo class 12 differential equations

A population grows according to dP/dt = 0.1P. If P(0)=1000, then P(t) is:

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A population grows according to dP/dt = 0.1P. If P(0)=1000, then P(t) is:

  • A. 1000e^(0.1t)
  • B. 1000e^(-0.1t)
  • C. 1000+0.1t
  • D. 1000t

Answer: A) 1000e^(0.1t)

Explanation: Standard exponential growth solution is P=P₀e^(kt).

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