Student Project: Logistic Equation with a Threshold Population An improvement to the logistic model includes a threshold population. The threshold population is defined to be the minimum population that is necessary for the species to survive. We use the variable T to represent the threshold population. A differential equation that incoqoraes both the threshold population T and carrying capacity K is d P d t = − r P ( 1 − P K ) ( 1 − P T ) (4.12) where r represents the growth rate. as before. 2. Draw the direction field for the differential equation from step 1, along with several solutions for different initial populations. What arc the constant solutions of the differential equation? What do these solutions correspond to In the original population model (I.e., In a biological context)?
Student Project: Logistic Equation with a Threshold Population An improvement to the logistic model includes a threshold population. The threshold population is defined to be the minimum population that is necessary for the species to survive. We use the variable T to represent the threshold population. A differential equation that incoqoraes both the threshold population T and carrying capacity K is d P d t = − r P ( 1 − P K ) ( 1 − P T ) (4.12) where r represents the growth rate. as before. 2. Draw the direction field for the differential equation from step 1, along with several solutions for different initial populations. What arc the constant solutions of the differential equation? What do these solutions correspond to In the original population model (I.e., In a biological context)?
Student Project: Logistic Equation with a Threshold Population An improvement to the logistic model includes a threshold population. The threshold population is defined to be the minimum population that is necessary for the species to survive. We use the variable T to represent the threshold population. A differential equation that incoqoraes both the threshold population T and carrying capacity K is
d
P
d
t
=
−
r
P
(
1
−
P
K
)
(
1
−
P
T
)
(4.12)
where r represents the growth rate. as before.
2. Draw the direction field for the differential equation from step 1, along with several solutions for different initial populations. What arc the constant solutions of the differential equation? What do these solutions correspond to In the original population model (I.e., In a biological context)?
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