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A scientist observes a population of bacteria in a petri dish. The population grows exponentially, doubling every 2hours. After 4hours of observation, there are about 6,000 bacteria.Which equation can you use to estimate n, the number of bacteria that were originally in the petri dish?

Question

A scientist observes a population of bacteria in a petri dish. The population grows exponentially, doubling every 2hours. After 4hours of observation, there are about 6,000 bacteria.Which equation can you use to estimate n, the number of bacteria that were originally in the petri dish?

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Solution

The exponential growth of a population can be described by the equation n = P * 2^(t/T), where:

  • n is the final amount of bacteria
  • P is the initial amount of bacteria (what we're trying to find)
  • t is the time that has passed
  • T is the doubling time

We know that n = 6000, t = 4 hours, and T = 2 hours. Substituting these values into the equation gives us:

6000 = P * 2^(4/2)

Solving this equation will give us the initial amount of bacteria, P.

This problem has been solved

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