a. Explanation Given: It is given that bacteria are grown on agar plates and form circular colonies and it is proportional to the number of bacteria contains. The population changes according to the equation N t + 1 = N t + 1 where I is the input of new individuals and is proportional to the circumference of the colony, with proportionality constant R . Concept Used: In this we have to know about the graph analysis and difference equation and concept about the area. We have use the formula of A t = π r t 2 , I = RC and N t + 1 = N t + 1 . Calculation: We ‘ re given the formula N t + 1 = N t + 1 .We need to find I in terms of N t .The problem states that I is proportional to the circumference of the bacteria colony. So, I = R C ,where R is the proportionally constant and C is the circumference of the colony. Now, we need to eliminate the variable C . To do this, we ‘re going to go back to the information in the beginning of the problem. The area of the colony is proportional to the number of bacteria it contains. So, A t = K N t ,where A t is the area of the colony at time t , K is the proportionally constant, and N t is the number of bacteria in the colony at time t . We know that for a circle, A t = π r t 2 b. To determine Draw the graph of N t , by some points assuming specific values for the proportionality constants.

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 1.6, Problem 35E

To determine

Calculate the recursion for the population size.

To determine

Draw the graph of Nt , by some points assuming specific values for the proportionality constants.

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Chapter 1.6, Problem 34E

Chapter 1.6, Problem 36E

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Calculate the recursion for the population size.

Solution Summary: The author explains how to calculate the recursion for the population size.

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Calculate the recursion for the population size.

Draw the graph of Nt , by some points assuming specific values for the proportionality constants.

Want to see the full answer?

Chapter 1 Solutions