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
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
Problem 5T
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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.
- 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
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).
- After how many hours will the two populations be equal in number? Give an exact answer (no decimals).
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