Two strains of bacteria are growing in separate Petri dishes. Initially, there are 300 Strain A bacteria and, from a prior experiment, you know that the population should double every 20 minutes. Having never worked with Strain B before, you monitor its growth over the first hour and notice that there are 200 bacteria after 30 minutes and 600 bacteria after 1 hour. Let t be the number of hours that have passed since the two populations of bacteria start growing. Express the number of strain A bacteria as a function of tt. Note: Your answer should be of the form PA(t)=Ce^(bt) PA(t)=Ce^(bt( for some numbers C and b. From your observations, you know that the population of Strain B bacteria after tt hours can be modelled by

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
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Two strains of bacteria are growing in separate Petri dishes. Initially, there are 300 Strain A bacteria and, from a prior experiment, you know that the population should double every 20 minutes.

Having never worked with Strain B before, you monitor its growth over the first hour and notice that there are 200 bacteria after 30 minutes and 600 bacteria after 1 hour.

  1. Let t be the number of hours that have passed since the two populations of bacteria start growing. Express the number of strain A bacteria as a function of tt. Note: Your answer should be of the form PA(t)=Ce^(bt) PA(t)=Ce^(bt( for some numbers C and b.
  2. From your observations, you know that the population of Strain B bacteria after tt hours can be modelled by
    PB(t)=(200/3)3^(2t) PB(t)=(200/3)3^(2t)
    How many strain B bacteria were present initially? (Round your answer down to the nearest integer).
  3. After how many hours will the two populations be equal in number? Give an exact answer (no decimals).
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