Chapter 5.4, Problem 86E

(a)

To determine

The models of the linear and quadratic form by means of regression capabilities of a graphing utility and to plot the data and the graph of the models for the data list of the values V of a mid-sized sedan from the year 2006 to the year 2012 and t is the variable that represents the time in years with $t=6$ for the year 2006.

$t$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
$V$	$23,406$	$20,596$	$18,851$	$17,001$	$15,226$	$14,101$	$12,841$

(b)

To determine

The representation of the slope of the linear model

$y_1=-1686.7857x+32561.3571$ where the values V of a mid-sized sedan from the year 2006 to the year 2012 and t is the variable that represents the time in years with $t=6$ for the year 2006.

$t$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
$V$	$23,406$	$20,596$	$18,851$	$17,001$	$15,226$	$14,101$	$12,841$

The graph of the linear model is:

(c)

To determine

The exponential models by means of regression capabilities of a graphing utility for the data list of the values V of a mid-sized sedan from the year 2006 to the year 2012 and t is the variable that represents the time in years with $t=6$ for the year 2006.

$t$	$6$	$7$	$8$	$9$	$10$	$11$	$12$
$V$	$23,406$	$20,596$	$18,851$	$17,001$	$15,226$	$14,101$	$12,841$

(d)

To determine

The horizontal asymptotes of the exponential model $y_3=40955.4556e^{-0.09735x}$.

(e)

To determine

To calculate: The rate of decrease in the value of sedan by the use of the exponential model

$y_3=40955.4556e^{-0.09735x}$ when $t=7$ and $t=11$.