A bacteria colony which is unrestricted in its growth will grow out in a circular manner. The population ?(?) of the colony at time t is directly proportional to the area of the circle. Suppose that a particular bacteria grows in such a way that the population is 1.3 times larger each day, and that initially (t=0) the colony has a diameter of 4 centimeter and a population of 7 million. a) Find the Population and Diameter of the colony on the fifth day. b) Find the Rate of Change of the Population and Diameter of the colony on the fifth day. c) Unrestricted growth models are often impractical as values will quickly become unreasonable. On what day does our model predict that the area of the bacteria colony will be 1 square mile?

Physics for Scientists and Engineers, Technology Update (No access codes included)
9th Edition
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
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Chapter1: Physics And Measurement
Section: Chapter Questions
Problem 1.29P
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A bacteria colony which is unrestricted in its growth will grow out in a circular manner. The population ?(?) of the colony at time t is directly proportional to the area of the circle. Suppose that a particular bacteria grows in such a way that the population is 1.3 times larger each day, and that initially (t=0) the colony has a diameter of 4 centimeter and a population of 7 million.

a) Find the Population and Diameter of the colony on the fifth day.

b) Find the Rate of Change of the Population and Diameter of the colony on the fifth day.

c) Unrestricted growth models are often impractical as values will quickly become unreasonable. On what day does our model predict that the area of the bacteria colony will be 1 square mile?

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