The size of poulation  after hours is .

(a).

Here represnts intial population is .

The  time minutes, hence hrs.

A cell of this bacterium in a nutrient-broth medium divides into two cells every minutes  : .

substitute   and in the  equation   .

.

Substitute in the equation .

The exponential growth rate .

(b).

Find number of cells after hours.

Number of cells after hours is .

Substitute and in the above equation .

.

Number of cells after hours is .

(c).

Find the number of cells after hours

Substitute in the equation .

After hours,number of cells is .

(d).

Find rate of growth aftrer   hours .

The rate of change of growth : .

Substitute and in the above equation .

.

.

The rate of change of growth after hours is .

(e).

Find the time when the population reaches cells.

Substitute , and in the equation .

hours.

The time when the population reaches cells is hours.

(a)The exponential growth rate .

(b) Number of cells after hours is .

(c) After hours,number of cells is .

(d) The rate of change of growth after hours is .

(e) The time when the population reaches cells is hours.