Chapter 2.6, Problem 47E

(a)

To determine

To calculate: The equation by use of graphing utility of the model of the form

$r\left(f\right)=a{f}^3+b{f}^2+cf+d$ for the table that shows the numbers of participant in the free lunch program $f$ and the reduced-price lunch program $r$ in the United States for the years 2007 through 2014.

Year	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$
$f$	$15.0$	$15.4$	$16.3$	$17.6$	$18.4$	$18.7$	$18.9$	$19.2$
$r$	$3.1$	$3.1$	$3.2$	$3.0$	$2.7$	$2.7$	$2.6$	$2.5$

(b)

To determine

To calculate: The value of $\frac{dr}{dt}$ for $t=9$ when number of participants in the lunch program will increase at the rate of 1.25 million participants per year of the model of the form

$r\left(f\right)=0.0096f^3-0.559f^2+10.54f-61.5$ for the table that shows the numbers of participant in the free lunch program $f$ and the reduced-price lunch program $r$ in the United States for the years 2007 through 2014.

Year	$2007$	$2008$	$2009$	$2010$	$2011$	$2012$	$2013$	$2014$
$f$	$15.0$	$15.4$	$16.3$	$17.6$	$18.4$	$18.7$	$18.9$	$19.2$
$r$	$3.1$	$3.1$	$3.2$	$3.0$	$2.7$	$2.7$	$2.6$	$2.5$