In the logistic model, N = 0 is a stableequilibrium point when...O a. r>0O b. K>0ОсС.r not equal to 0O d. r<0

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In the logistic model, N = 0 is a stable equilibrium point when ... а. r>0 O b. K>0 Ос r not equal to 0 С. O d. r<0

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...

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Question

In the logistic model, N = 0 is a stable
equilibrium point when...
O a. r>0
O b. K>0
Ос
С.
r not equal to 0
O d. r<0

Expert Solution

Step 1

The equilibrium point of a differential equation is the point where the rate of change is zero. For the differential equation $\frac{d y}{d x} = f (x)$ , the equilibrium point is determined by solving the equation $f (x) = 0$ . Let the equilibrium point be $x = x'$ . If $f' (x') < 0$ , $x = x'$ is stable. The negative sign of $f' (x')$ implies instability. When it equals zero, the equilibrium point is neutral. The logistic equation is one of the important differential equations having order 1. The population of a certain area is modeled through this equation.

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