## DESCRIPTION
## Instantaneous Rate of Change
## ENDDESCRIPTION

## KEYWORDS('instantaneous', 'rate of change', 'application', 'derivative')
## Tagged by YL

## DBsubject('Calculus')
## DBchapter('Differentiation')
## DBsection('Rates of Change in the Natural and Social Sciences')
## Date('')
## Author('')
## Institution('ASU')
## TitleText1('Calculus: Early Transcendentals')
## EditionText1('5')
## AuthorText1('Stewart')
## Section1('3.3')
## Problem1('')

## TitleText2('Calculus: Early Transcendentals')
## EditionText2('6')
## AuthorText2('Stewart')
## Section2('3.7')
## Problem2('')

DOCUMENT();

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

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

$a = random(15,25, 1);
$b = random(1,4,1);
$c = random(6,8,1);

TEXT(EV2(<<EOT));
If a person learns \(y\) items in \(x\) hours, as given by
\[ y = $a \sqrt[3]{x^2}, \]
find the rate of learning for a person at the end of:
$BR
(A) $b hours: \{ans_rule(30) \}
$BR
EOT

$ans = ((2*$a)/3)*($b**(-1/3));
ANS(num_cmp($ans));

TEXT(EV2(<<EOT));
(B) $c hours: \{ans_rule(30) \}
$BR
EOT

$ans = ((2*$a)/3)*($c**(-1/3));
ANS(num_cmp($ans));


ENDDOCUMENT();