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1. Suppose that the population of a certain type of bacteria, P. changes with time, t, according to the Limited Growth Model given by = k(M - P), P(0)= 10 million bacteria. %3D dt (a) Use the separation of variables method to find a formula for the population as a function of time. Assume that the initial population increases to 15 million bacteria after 0.5 hours, and that the carrying capacity of the system, M, is 20 million bacteria. (b) Check your particular solution. (c) Find the equilibrium population value(s) for this system, and determine their stability. (d) Find the change in population betweent-1 and t=2 hours using a definite integral.

1. Suppose that the population of a certain type of bacteria, P. changes with time, t, according to the Limited Growth Model given by = k(M - P), P(0)= 10 million bacteria. %3D dt (a) Use the separation of variables method to find a formula for the population as a function of time. Assume that the initial population increases to 15 million bacteria after 0.5 hours, and that the carrying capacity of the system, M, is 20 million bacteria. (b) Check your particular solution. (c) Find the equilibrium population value(s) for this system, and determine their stability. (d) Find the change in population betweent-1 and t=2 hours using a definite integral.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 14EQ
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1. Suppose that the population of a certain type of bacteria, P. changes with time, t, according to the Limited Growth Model given by = k(M - P), P(0)= 10 million bacteria. %3D dt (a) Use the separation of variables method to find a formula for the population as a function of time. Assume that the initial population increases to 15 million bacteria after 0.5 hours, and that the carrying capacity of the system, M, is 20 million bacteria. (b) Check your particular solution. (c) Find the equilibrium population value(s) for this system, and determine their stability. (d) Find the change in population betweent-1 and t=2 hours using a definite integral.
Transcribed Image Text:1. Suppose that the population of a certain type of bacteria, P. changes with time, t, according to the Limited Growth Model given by = k(M - P), P(0)= 10 million bacteria. %3D dt (a) Use the separation of variables method to find a formula for the population as a function of time. Assume that the initial population increases to 15 million bacteria after 0.5 hours, and that the carrying capacity of the system, M, is 20 million bacteria. (b) Check your particular solution. (c) Find the equilibrium population value(s) for this system, and determine their stability. (d) Find the change in population betweent-1 and t=2 hours using a definite integral.
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