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The formula to estimate organic growth is Pf=P0 . e^rt

MegaVax manufactures vaccinations. The microbe jagus rashii, is being grown for a vaccine against a new strain of influenza. Jagus rashii grows at a rate of 25.0% per hour. How long will it take for a culture of 1,349 jagus rashii to grow to a population of 75,709?

Express your answer to the nearest hundredth of an hour.

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mhanifa

Answer:

  • 16.12 hr

Step-by-step explanation:

If I got it right, we have:

  • Formula Pf = P0*e^(rt)
  • Pf = 75709
  • P0 = 1349
  • r = 25% = 0.25
  • t = ?

Substitute the given values and solve for t:

  • 75709 = 1349*e^(0.25t)
  • e^(0.25t) = 75709/1349
  • e^(0.25t) = 56.1223
  • ln e^(0.25t) = ln 56.1223
  • 0.25t = 4.03
  • t = 4.03/0.25
  • t = 16.12 hr

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