View of /trunk/NationalProblemLibrary/ASU-topics/setDerivativeBasicFunctions/3-4-86.pg

    1 ## DESCRIPTION
    2 ## Instantaneous Rate of Change
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('instantaneous', 'rate of change', 'application', 'derivative')
    6 ## Tagged by YL
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differentiation')
   10 ## DBsection('Rates of Change in the Natural and Social Sciences')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('ASU')
   14 ## TitleText1('Calculus: Early Transcendentals')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('3.3')
   18 ## Problem1('')
   19 
   20 DOCUMENT();
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showpartialcorrectanswers = 1;
   32 
   33 $a = random(.3,.9, .1);
   34 $b = random(1,5,1);
   35 $c = random(7,12,1);
   36 
   37 TEXT(EV2(<<EOT));
   38 A coal-burning electrical generating plant emits sulfur dioxide
   39 into the surrounding air.  The concentration \(C(x)\), in parts per
   40 million, is approximately given by the function
   41 \[ C(x) = \frac{$a}{x^2}, \]
   42 where \(x\) is the distance away from the plant in miles.
   43 $BR
   44 The instantaneous rate of change of the sulfur dioxide
   45 concentration:
   46 $BR
   47 (A) $b miles from the plant = \{ans_rule(30) \}
   48 $BR
   49 EOT
   50 
   51 $ans = (-2)*$a*(($b)**(-3));
   52 ANS(num_cmp($ans));
   53 
   54 TEXT(EV2(<<EOT));
   55 (B) $c miles from the plant = \{ans_rule(30) \}
   56 $BR
   57 EOT
   58 
   59 $ans = -2*$a*($c**(-3));
   60 ANS(num_cmp($ans));
   61 
   62 
   63 ENDDOCUMENT();