The value of an item after years is , .

(a)

Graph the function on .

Graph:

(b)

The value of an item after years is .

Apply derivative on each side with respect to .

.

The rate of change of with respect to is .

When the rate of change of :

Substitute in .

.

When the rate of change of :

Substitute in .

.

(c)

Find the tangent lines at and .

When .

.

The point is .

Point-slope form of line equation: .

Substitute and in point-slope form.

The tangent line equation when is .

When .

.

The point is .

Substitute and in point-slope form.

.

The tangent line equation when is .

Graph the tangent lines.

(a)

Graph:

Graph the function on .

.

(b)

and .

(c)

Graph:

Graph the tangent line equation at is .

The tangent line equation at is .

.