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Bacteria are often grown on agar plates and form circular colonies. The area of a colony is proportional to the number of bacteria it contains. The agar (a gelatinous substance obtained from red seaweed) is the resource that bacteria use to reproduce and so only those bacteria on the edge of the colony can produce new offspring. Therefore the population dynamics are Nt+1 = Nt + I, where I is the input of new individuals and is proportional to the circumference of the colony, with proportionality constant R. (Let the area of the colony be directly proportional to the number of bacteria by a constant of proportionality K. Also let K = 2√.) (a) Derive the recursion for the population dynamics. (Write your answers in terms of N, Nt, K, and R.) Nt+1 = X

Bacteria are often grown on agar plates and form circular colonies. The area of a colony is proportional to the number of bacteria it contains. The agar (a gelatinous substance obtained from red seaweed) is the resource that bacteria use to reproduce and so only those bacteria on the edge of the colony can produce new offspring. Therefore the population dynamics are Nt+1 = Nt + I, where I is the input of new individuals and is proportional to the circumference of the colony, with proportionality constant R. (Let the area of the colony be directly proportional to the number of bacteria by a constant of proportionality K. Also let K = 2√.) (a) Derive the recursion for the population dynamics. (Write your answers in terms of N, Nt, K, and R.) Nt+1 = X

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Bacteria are often grown on agar plates and form circular colonies. The area of a colony is proportional to the number of bacteria it contains. The agar (a gelatinous substance obtained from red seaweed) is the resource that bacteria use to reproduce and so only those bacteria on the edge of the colony can produce new offspring. Therefore the population dynamics are Nt+1 Nt + I, where I is the input of new individuals and is proportional to the circumference of the colony, with proportionality constant R. Let the area of the colony be directly proportional to the number of bacteria by a constant of proportionality k. Also let K = 2√ K.) (a) Derive the recursion for the population dynamics. (Write your answers in terms of N, Nt, K, and R.) Nt+1 =
Transcribed Image Text:Bacteria are often grown on agar plates and form circular colonies. The area of a colony is proportional to the number of bacteria it contains. The agar (a gelatinous substance obtained from red seaweed) is the resource that bacteria use to reproduce and so only those bacteria on the edge of the colony can produce new offspring. Therefore the population dynamics are Nt+1 Nt + I, where I is the input of new individuals and is proportional to the circumference of the colony, with proportionality constant R. Let the area of the colony be directly proportional to the number of bacteria by a constant of proportionality k. Also let K = 2√ K.) (a) Derive the recursion for the population dynamics. (Write your answers in terms of N, Nt, K, and R.) Nt+1 =
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