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dN//dt=rN((K-N)/K) A-population at tim...

`dN//dt=rN((K-N)/K)`
A-population at time t
B-Intrinsic rate of natural increase
C-carrying capacity
Identify A,B, and C from given equation

A

`{:(A,B,C),(N,K,r):}`

B

`{:(A,B,C),(N,r,K):}`

C

`{:(A,B,C),(K,N,r):}`

D

`{:(A,B,C),(K,r,N):}`

Text Solution

AI Generated Solution

The correct Answer is:
To identify A, B, and C from the equation \( \frac{dN}{dt} = rN\left(\frac{K-N}{K}\right) \), we can analyze the components of the equation step by step. ### Step 1: Identify A (Population at time t) In the equation, \( N \) represents the population size at a given time \( t \). Therefore, we can conclude that: - **A = N** (Population at time t) ### Step 2: Identify B (Intrinsic rate of natural increase) The term \( r \) in the equation represents the intrinsic rate of natural increase of the population. This is the rate at which the population would grow if there were no limitations on resources. Thus: - **B = r** (Intrinsic rate of natural increase) ### Step 3: Identify C (Carrying capacity) The term \( K \) in the equation refers to the carrying capacity of the environment, which is the maximum population size that the environment can sustain indefinitely. Hence: - **C = K** (Carrying capacity) ### Final Identification - **A = N** (Population at time t) - **B = r** (Intrinsic rate of natural increase) - **C = K** (Carrying capacity)
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