(a)

The size of pupulation after hours is .

Here represents intial pupulation is .

After an hour the pupulation is increased to .i.e

Substitute and  and   in the equation .

The exponential growth rate .

The no.of population after hours.

Number of cells after hours is .

Substitute and in the above equation .

Number of cells after hours is.

(b).

Find the no.of bacteria after hrs 

Substitute in the equation

.

After hours,number of cells is .

(c).

Find the rate of growth after hrs .

The rate of change of growth : .

Substitute and in the above equation .

The rate of change of growth after hours is .

(d).

Find the time when the population reaches .

Substitute and and im the equation .

The time when the population reaches   is hours.

(a).Number of cells after hours is.

(b).After hours,number of cells is .

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

(d).The time when the population reaches   is hours.