## DESCRIPTION
## Calculus
## ENDDESCRIPTION

## KEYWORDS('calculus', 'derivative')
## Tagged by YL

## DBsubject('Calculus')
## DBchapter('Single Variable')
## DBsection('Differentiation')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('Calculus')
## EditionText1('5e')
## AuthorText1('Stewart')
## Section1('')
## Problem1('')

DOCUMENT();

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(beginproblem());
$showpartialcorrectanswers = 1;

$a = random(.3,.9, .1);
$b = random(1,5,1);
$c = random(7,12,1);

TEXT(EV2(<<EOT));
A coal-burning electrical generating plant emits sulfur dioxide
into the surrounding air.  The concentration \(C(x)\), in parts per
million, is approximately given by the function
\[ C(x) = \frac{$a}{x^2}, \]
where \(x\) is the distance away from the plant in miles.
$BR
The instantaneous rate of change of the sulfur dioxide
concentration:
$BR
(A) $b miles from the plant = \{ans_rule(30) \}
$BR
EOT

$ans = (-2)*$a*(($b)**(-3));
ANS(num_cmp($ans));

TEXT(EV2(<<EOT));
(B) $c miles from the plant = \{ans_rule(30) \}
$BR
EOT

$ans = -2*$a*($c**(-3));
ANS(num_cmp($ans));


ENDDOCUMENT();