(a)

The logistic growth model of bacterium after  hours is  eagles.

Substitute   in logistic growth model to find the carrying capacity of the environment.

Therefore.the carrying capacity of the environment is  eagles.

(b)

The standard logistic growth model of population after  years is  .

The logistic growth model of eagle after  years is eagles.

Compare the logistic model with standard logistic model  ,and .

The growth rate is for standard logistic model is .

Therefore, the growth rate of the eagle is  per year.

The growth rate of the eagle is  per year.

(c)

Find the population after years.

The equation is  .

Substitute .

Therefore,the size of population after years is  eagles.

(d)

Find the time when the size of population is eagles.

The equation is  .

Therefore, the population reaches  eagles after   years.

(e)

The function is .

The carrying capacity of the environment is  grams.

One-half the carrying capacity is grams.

The time when population size reaches  grams .

Substituting .

Therefore, the population size of bacteria reaches one-half the carrying capacity after  years.

(a) The carrying  capacity of the environment is  eagles.

(b) The growth rate of the eagle is  per year.

(c) The size of population after years is  eagles.

(d) The populationreaches  eagles after   years.

(e) The population size of bacteria reaches one-half the carrying capacity after  years.