$\"\"$

\

(a)

\

Statement :

\

The rate of change $\"\"$ is propotinal to the difference between $\"\"$ and $\"\"$ .

\

$\"\"$ is proportional to $\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

Apply integral on each side.

\

$\"\"$

\

$\"\"$

\

Power rule of integrals : $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(b)

\

The direction field satisfies $\"\"$ along $\"\"$ .

\

The differential equation matches with the slope field $\"\"$ .

\

$\"\"$

\

(c)

\

Verification :

\

Graph the differential equation $\"\"$ .

\

Graph :

\

$\"\"$

\

Observe the graph :

\

The differential equation matches with the slope field $\"\"$ .

\

$\"\"$

\

(a) $\"\"$ .

\

(b) The differential equation matches with the slope field $\"\"$ .

\

(c) Graph:

\

$\"\"$

\

The differential equation matches with the slope field $\"\"$ .