Question

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.

Answer 1

• 16.12 hr

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