imo class 12 differential equations

In a culture, the bacteria count is 100,000. The number is increasing at a rate proportional to the number present. In 2 hours, it increases by 10%. The DE is dN/dt = kN. What is N at time t=0?

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In a culture, the bacteria count is 100,000. The number is increasing at a rate proportional to the number present. In 2 hours, it increases by 10%. The DE is dN/dt = kN. What is N at time t=0?

  • A. 10,000
  • B. 100,000
  • C. 110,000
  • D. 0

Answer: B) 100,000

Explanation: The initial count at t=0 is explicitly given in the problem as 100,000.

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