(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.