$\"\"$

\

(a)

\

Model equation $\"\"$ .

\

Graph:

\

Graph the data using regression capabilities:

\

$\"\"$

\

Observe the graph:

\

The linear model equation is $\"\"$ .

\

Model equation $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

The model equation is $\"\"$ .

\

Model equation $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

The model equation is $\"\"$ .

\

$\"\"$

\

The model equation is $\"\"$ .

\

Model equation $\"\"$ .

\

$\"\"$

\

Observe the graph:

\

The model equation is $\"\"$ .

\

$\"\"$

\

(b)

\

Graph:

\

Graph the linear model equation is $\"\"$ and data:

\

$\"\"$

\

Graph:

\

Graph the logarithm model equation is $\"\"$ and data:

\

$\"\"$

\

Graph:

\

Graph the exponential model equation is $\"\"$ and data:

\

$\"\"$

\

Graph:

\

Graph the quadratic model equation is $\"\"$ and data:

\

$\"\"$

\

Observe the graphs:

\

The model $\"\"$ is best fits the data.

\

$\"\"$

\

(c)

\

The linear model equation is $\"\"$ .

\

The standard form of linear equation is $\"\"$ .

\

Where $\"\"$ is slope of the equation and $\"\"$ is a constant.

\

Compare $\"\"$ with $\"\"$ .

\

The slope of the linear model equation is $\"\"$ .

\

The slope of the linear model is positive.

\

Therefore, the rate of organ transplants was increasing at a steady rate during the years $\"\"$ to $\"\"$ .

\

$\"\"$

\

(d)

\

Find the rate of change of each of the models for the year $\"\"$ .

\

The linear model equation is $\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

The rate of change of linear model equation is $\"\"$ .

\

\

The logarithm model equation is $\"\"$ .

\

The rate of change of logarithm model equation is $\"\"$ .

\

\

The exponential model equation is $\"\"$ .

\

The rate of change of exponential model equation is $\"\"$ .

\

$\"\"$

\

$\"\"$ .

\

\

The quadratic model equation is $\"\"$ .

\

The rate of change of quadratic model equation is $\"\"$ .

\

$\"\"$ .

\

\

The rate of change of each of the models for the year $\"\"$ .

\

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

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

$\"\"$ .

\

Observe the $\"\"$ and $\"\"$ values at $\"\"$ .

\

$\"\"$ Model is increasing at the greatest rate in $\"\"$ .

\

$\"\"$

\

(a)

\

Model equation $\"\"$ .

\

Graph:

\

$\"\"$

\

The linear model equation is $\"\"$ .

\

Model equation $\"\"$ .

\

$\"\"$

\

The model equation is $\"\"$ .

\

Model equation $\"\"$ .

\

$\"\"$

\

The model equation is $\"\"$ .

\

$\"\"$

\

The model equation is $\"\"$ .

\

Model equation $\"\"$ .

\

$\"\"$

\

The model equation is $\"\"$ .

\

(b)

\

Graph of $\"\"$ :

\

$\"\"$

\

Graph of $\"\"$ :

\

$\"\"$

\

Graph of $\"\"$ :

\

$\"\"$

\

Graph of $\"\"$ :

\

$\"\"$

\

The model $\"\"$ is best fits the data.

\

(c)

\

The slope of the linear model is positive.

\

Therefore, the rate of organ transplants was increasing at a steady rate during the years $\"\"$ to $\"\"$ .

\

(d) $\"\"$ Model is increasing at the greatest rate in $\"\"$ .