(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 .