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    1 ## DBsubject('Calculus')
    2 ## DBchapter('Introduction to Differential Equations')
    3 ## DBsection('Parametric Equations')
    4 ## KEYWORDS('calculus', 'parametric', 'parametric equations')
    5 ## TitleText1('Calculus: Early Transcendentals')
    6 ## EditionText1('2')
    7 ## AuthorText1('Rogawski')
    8 ## Section1('11.1')
    9 ## Problem1('11')
   10 ## Author('Christopher Sira')
   11 ## Institution('W.H.Freeman')
   12 
   13 DOCUMENT();
   14 loadMacros("PG.pl","PGbasicmacros.pl","PGanswermacros.pl");
   15 loadMacros("Parser.pl");
   16 loadMacros("freemanMacros.pl");
   17 
   18 $context = Context("Point");
   19 $context->variables->add(t=>'Real');
   20 #$context->variables->add(x=>'Real');
   21 $context->flags->set(reduceConstants=>0);
   22 $context->flags->set(reduceConstantFunctions=>0);
   23 
   24 $a = Real(random(-5, -2, 1));
   25 $b = Real(random(2, 6, 1));
   26 $c = Real(random(2, 5, 1));
   27 
   28 $xform = Formula("e**($a * t)")->reduce;
   29 $txform = Formula("ln(x)/$a")->reduce;
   30 
   31 $yform = Formula("$b * e**($c * t)")->reduce;
   32 
   33 $ans = $yform->substitute(t=>$txform)->reduce();
   34 
   35 
   36 Context()->texStrings;
   37 BEGIN_TEXT
   38 \{ beginproblem() \}
   39 \{ textbook_ref_exact("Rogawski ET 2e", "11.1","11") \}
   40 $PAR
   41 Express \( x = $xform \), \( y = $yform \) in the form \( y = f(x) \) by eliminating the parameter.
   42 $PAR
   43 y = \{ans_rule()\}
   44 END_TEXT
   45 Context()->normalStrings;
   46 
   47 ANS($ans->cmp);
   48 
   49 Context()->texStrings;
   50 SOLUTION(EV3(<<'END_SOLUTION'));
   51 $PAR
   52 $SOL
   53 We eliminate the parameter.  Since \( x = $xform \), we have \( t = $txform \).  Substituting into \( y = $yform \) we obtain
   54 $PAR
   55 \( y = $ans \)
   56 END_SOLUTION
   57 
   58 ENDDOCUMENT();