(a).

The function is , where represents the number of years.

(1). Draw the coordinate plane.

(2). Graph the function .

Graph :

Observe the graph:

At , the value of the function .

Therefore, the value of the car purchased after  years is .

(b).

The function is .

The rate of change is the first derivative of that function.

Consider .

Apply derivative on each side with respect to .

.

Substitute in the above equation.

Substitute in .

(c).

Consider .

The horizontal asymptote of is .

Thus, the horizontal asymptote is .

(1). Draw the coordinate plane.

(2). Graph the function .

Graph :

Note : The dashed line indicates the horizontal asymptote.

Observe the graph :

The graph has a horizontal asymptote at .

This means that as , .

Because the value of the car cannot keep decresing foreever.

Value of car cannot be negative, It will become very close to zero.

(a).

The the car purchased after  years is .

(b).

The rate of change in value of the car when is .

The rate of change in value of the car when is .

(c).

Graph : 

Horizontal asymptote is .

This means that as , .

Value of car cannot be negative, It will become very close to zero.