Bacteria colonies on agar plates Bacteria are often grown on agar plates and form

Chapter 1, Problem 35

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Bacteria colonies on agar plates 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 changes according to the equation Nt11 Nt 1 I, where I is the input of new individuals and is proportional to the circumference of the colony, with proportionality constant R. (a) Derive the recursion for the population size. (b) Plot some points on the graph of Nt, assuming specific values for the proportionality constants.