Question

During the exponential phase, E. coli bacteria in a culture increase in number at a rate proportional to the current population. If the growth rate is 1.9% per minute and the current population is 172.0 million, what will the population be 7.2 minutes from now?

Answer 1

Answer:

  197.2 million

Step-by-step explanation:

The appropriate exponential equation for the population is ...

  p(t) = 172.0e^(0.019t)

Then we can compute for t=7.2:

  p(7.2) = 172.0e^(0.019·7.2) ≈ 172.0·1.146599 ≈ 197.2

7.2 minutes from now, the population will be about 197.2 million.

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For continuous growth (or continuous compounding), the exponential formula is ...

  f(t) = (value at t=0)×e^(rt)

where r is the growth rate in one unit of time, and t is the number of time periods.