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A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____
[Answer in integer]
(Hint: maximum population growth rate occurs when N = K/2).
[Answer in integer]
(Hint: maximum population growth rate occurs when N = K/2).
Correct answer is between '12,13'. Can you explain this answer?
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Verified Answer
A population is showing logistic growth. If the carrying capacity is 5...
In the question you’re given the following information:
K = 500, r = 0.1
Maximum population growth occurs at K/2
Therefore, the maximum population size = K/2 = 500/2 = 250
Logistic growth equation for a population
dN/dt = rN[1 – N/K]
dN/dt = (0.1) (250) [1 – (250)/500)] dN/dt = 12.5 individuals/month
K = 500, r = 0.1
Maximum population growth occurs at K/2
Therefore, the maximum population size = K/2 = 500/2 = 250
Logistic growth equation for a population
dN/dt = rN[1 – N/K]
dN/dt = (0.1) (250) [1 – (250)/500)] dN/dt = 12.5 individuals/month
Most Upvoted Answer
A population is showing logistic growth. If the carrying capacity is 5...
Logistic Growth:
Logistic growth is a type of population growth where the population size initially grows exponentially but eventually levels off due to environmental factors. It is characterized by an S-shaped growth curve.
Carrying Capacity:
The carrying capacity (K) is the maximum number of individuals that a given environment can support sustainably. It represents the equilibrium population size that can be maintained over the long term.
Population Growth Rate:
The population growth rate (r) represents the rate at which the population size increases or decreases over time. It is usually expressed in terms of the number of individuals added or lost per individual per unit of time.
Maximum Population Growth Rate:
The maximum population growth rate occurs when the population size is half of the carrying capacity (N = K/2). At this point, the population is growing at its fastest rate and the growth rate gradually decreases as the population approaches the carrying capacity.
Calculating the Maximum Population Growth Rate:
Given that the carrying capacity (K) is 500 and the growth rate (r) is 0.1 individuals/(individuals x month), we can calculate the maximum population growth rate.
1. Substitute the carrying capacity value into the equation N = K/2:
N = 500/2
N = 250
2. Calculate the maximum population growth rate using the formula:
Growth rate (r) = r * (1 - N/K)
Growth rate (r) = 0.1 * (1 - 250/500)
Growth rate (r) = 0.1 * (1 - 0.5)
Growth rate (r) = 0.1 * 0.5
Growth rate (r) = 0.05 individuals/(individuals x month)
Conclusion:
The maximum population growth rate for this population, based on the given carrying capacity and growth rate, is 0.05 individuals/(individuals x month). However, the provided answer range of '12-13' does not seem to be related to the given information. It is possible that there is an error or misunderstanding in either the question or the answer provided.
Logistic growth is a type of population growth where the population size initially grows exponentially but eventually levels off due to environmental factors. It is characterized by an S-shaped growth curve.
Carrying Capacity:
The carrying capacity (K) is the maximum number of individuals that a given environment can support sustainably. It represents the equilibrium population size that can be maintained over the long term.
Population Growth Rate:
The population growth rate (r) represents the rate at which the population size increases or decreases over time. It is usually expressed in terms of the number of individuals added or lost per individual per unit of time.
Maximum Population Growth Rate:
The maximum population growth rate occurs when the population size is half of the carrying capacity (N = K/2). At this point, the population is growing at its fastest rate and the growth rate gradually decreases as the population approaches the carrying capacity.
Calculating the Maximum Population Growth Rate:
Given that the carrying capacity (K) is 500 and the growth rate (r) is 0.1 individuals/(individuals x month), we can calculate the maximum population growth rate.
1. Substitute the carrying capacity value into the equation N = K/2:
N = 500/2
N = 250
2. Calculate the maximum population growth rate using the formula:
Growth rate (r) = r * (1 - N/K)
Growth rate (r) = 0.1 * (1 - 250/500)
Growth rate (r) = 0.1 * (1 - 0.5)
Growth rate (r) = 0.1 * 0.5
Growth rate (r) = 0.05 individuals/(individuals x month)
Conclusion:
The maximum population growth rate for this population, based on the given carrying capacity and growth rate, is 0.05 individuals/(individuals x month). However, the provided answer range of '12-13' does not seem to be related to the given information. It is possible that there is an error or misunderstanding in either the question or the answer provided.
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A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer?
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A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer?.
A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer?.
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A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer?, a detailed solution for A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer? has been provided alongside types of A population is showing logistic growth. If the carrying capacity is 500 for this population and r = 0.1 individuals/ (individuals x month), the maximum population growth rate for the population will be _____[Answer in integer](Hint: maximum population growth rate occurs when N = K/2).Correct answer is between '12,13'. Can you explain this answer? theory, EduRev gives you an
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