The population of a culture of bacteria is modeled by the logistic equation P(t)= \frac{14,250}{1+29e^{-0.62t}. To the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? What is the carrying capacity? What is the initial population for the model?
The population of a culture of bacteria is modeled by the logistic equation P(t)= \frac{14,250}{1+29e^{-0.62t}. To the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? What is the carrying capacity? What is the initial population for the model?
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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The population of a culture of bacteria is modeled by the logistic equation
P(t)= \frac{14,250}{1+29e^{-0.62t}.
To the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? What is the carrying capacity? What is the initial population for the model? Why a model like P(t)=P_0 \ e^{Kt} , where P_0 is the initial population, would not be plausible? What are the virtues of the logistic model?
Go to www.desmos.com/calculator and type
y = 14250 / (1 + 29 . e-0.62 x). {0 < x < 15} {0 < y < 15000}
y = 14300 {0 < x < 15}
(you will find the command “\div” in the desmos calculator after selecting “14250”, or you type “/” after selecting “14250”, and you will also find the function “exp” ). Adjust the x and y axes settings to 0 < x < 15 and 0 < y < 15000. Plot the graph you have obtained (you can use a screenshot, save as image, and copy it into word). If you need, or if you want, go to the Course Forum and tell us something about this plotting task.
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