Question
In a certain isolated population p (t) the rate of population growth is equal to
, where k and ɛ are both positive constants. If p (0) = 1, then find the limiting population as t→ ∞.
Answer :
Word Count : 246
We are given the differential equation: \[ \frac{dp}{dt} = p - \frac{k}{\varepsilon} p^2 \] ### Step 1: Find the Equilibrium Points To determine the limiting population as \( t \to \infty \), we set \( \frac{dp}{dt} = 0 \): \[ p - \frac{k}{\varepsilon} p^2 = 0 \] Factorizing: \[ p \left( 1 - \frac{k}{\varepsilon} p \right) = 0 \] Thus, the ________ ______ ____ ___ ________ ____ ___.
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_______ _______ ____ __________ _______ __________.
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We are given the differential equation: \[ \frac{dp}{dt} = p - \frac{k}{\varepsilon} p^2 \] ### Step 1: Find the Equilibrium Points To determine the limiting population as \( t \to \infty \), we set \( \frac{dp}{dt} = 0 \): \[ p - \frac{k}{\varepsilon} p^2 = 0 \] Factorizing: \[ p \left( 1 - \frac{k}{\varepsilon} p \right) = 0 \] Thus, the ________ ______ ____ ___ ________ ____ ___.
_____ __________ ____ ______ _______ _______ _________ __________ _______ ______ ____.
_______ ___ ________ _____ _____.
_________ ________ ______ ___ _________ _____ _______ _____ _____ _____ ____ ________.
__________ _____ ____ ______ _____ ____.
________ _________ ____ _____ ________ __________ ___.
_____ _____ _____ ______ _______.
_________ ________ _______ _______ __________ ________ _______ ________ _______ ____.
________ _____ ________ ____ _______.
_________ ___ ________ ________ ____ ______ _________ ______ _____ _____.
____ ___ ________ ______ ____.
__________ _______ _______ ________ _______.
______ ___ __________ _________ ______ ________ __________ _______ ___.
_________ ______ _________ _______ _____.
_______ ________ ___ ______ _______ ______ ______ ___ _____ _______ __________ __________.
___ __________ ____ ______ ____.
_____ __________ _____ _______ _____ ____ _______ _______.
_______ _____ _________ __________ _______ _____.
____ ________ ______ _________ ___ _____ _________ ___ ________ ___.
_____ _____ _______ __________ _______ _______ _________ _______ ____.
__________ _____ _______ ___ _________ _____.
_______ __________ _________ ____ _____ __________ ________ _____ ______ _____ _____.
_______ ______ _____ _________ _________ _____ ___ _______ ________ __________.
_______ _______ ____ __________ _______ __________.
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