(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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