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| PAGE: 637 | SET: Exercises | PROBLEM: 1 |
(a)
Logistic equation is 
, where 
measured in weeks.
Logistic differential equation with carrying capacity 
is 
.
Rewrite the logistic equation as
.
.
Compare above equation with 
.
Therefore, 
and 
.
(b)
Observe the dirction field in the graph:
Slopes are close to zero when 
or 
.
Slopes are largest on the line 
.
Solutions are increasing in the interval 
.
Solutions are decreasing in the imterval 
.
(c)
Graph the directional field to graph the solutions of 
and 
.
Observe the dirction field in the graph:
All the solutions have the slopes closes to zero.
Some solutions are increasing and some are decreasing.
Solutions of 
and 
have inflection point at .
(d)
Slopes are close to zero when 
or 
.
Thus, and are equilibrium solutions.
Other solutions are differ from the above as they are moving away from towards .
(a) 
and 
.
(b)
Slopes are close to zero when or .
Slopes are largest on the line 
.
Solutions are increasing in the interval 
.
Solutions are decreasing in the imterval 
.
(c) Graph:
(d)
and are equilibrium solutions.
Other solutions are differ from the above as they are moving away from towards .
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