$\"\"$

\

The rate of change of population of bacteria is $\"\"$ .

\

$\"\"$

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$

\

Let $\"\"$ .

\

Apply derivative on each side with respect to $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$ .

\

The equation of population is $\"\"$ .

\

$\"\"$

\

The initial population of bacteria is $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$ .

\

The population of bacteria at time $\"\"$ is $\"\"$ .

\

$\"\"$

\

Find the population of bacteria at time $\"\"$ .

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$ .

\

The population of bacteria at time $\"\"$ is $\"\"$ .

\

$\"\"$

\

The population of bacteria at time $\"\"$ is $\"\"$ .

\

The population of bacteria at time $\"\"$ is $\"\"$ .