(a)

The logistic growth model of bacterium after  hours is  grams.

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

Therefore, the carrying  capacity of the environment is  grams.

(b)

The standard logistic growth model of population after  hours is  .

The logistic growth model of bacterium after  hours is  grams.

Compare the logistic model with standard logistic model  ,and .

The growth rate is for standard logistic model is .

Therefore, the growth rate of the bacteria is  per hour.

The growth rate of the bacteria is  per hour.

(c)

Find the size of initial population.

The equation is .

Substitute .

Therefore, the initial population size of bacteria is  grams.

(d)

Find the population after hours.

The equation is .

Substitute .

Therefore, the size of population after  hours is  grams.

(e)

Find the time when the size of population is .

The equation is  .

Equate .

Therefore, the population size of bacteria reaches   grams after  hours.

(f)

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  hours.

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

(b) The growth rate of the bacteria is  per hour.

(c) The initial population size of bacteria is  grams.

(d) The size of population after  hours is  grams.

(e) The population size of bacteria is   grams after  hours.

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