View of /trunk/NationalProblemLibrary/Dartmouth/setStewartCh10S4/problem_1.pg

    1 ## DESCRIPTION
    2 ## Calculus
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('exponential growth' 'population')
    6 ## Tagged by tda2d
    7 
    8 ## DBsubject('Calculus')
    9 ## DBchapter('Differential Equations')
   10 ## DBsection('Exponential Growth and Decay')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Dartmouth')
   14 ## TitleText1('Calculus')
   15 ## EditionText1('5')
   16 ## AuthorText1('Stewart')
   17 ## Section1('10.4')
   18 ## Problem1('')
   19 
   20 
   21 DOCUMENT();
   22 loadMacros("PG.pl",
   23            "PGbasicmacros.pl",
   24            "PGchoicemacros.pl",
   25            "PGanswermacros.pl",
   26            "PGauxiliaryFunctions.pl",
   27            "PGgraphmacros.pl",
   28            "Dartmouthmacros.pl");
   29 
   30 
   31 ## Do NOT show partial correct answers
   32 $showPartialCorrectAnswers = 0;
   33 
   34 $initial= random(300,900,100);
   35 $later = random(3000,10000,1000);
   36 $t1 = random(3,9);
   37 
   38 
   39 ## Ok, we are ready to begin the problem...
   40 ##
   41 TEXT(beginproblem());
   42 
   43 
   44 BEGIN_TEXT
   45 $BR
   46 
   47 A bacteria culture starts with $initial bacteria and grows at a rate
   48 proportional to its size.  After $t1 hours, there are $later bacteria.
   49 $PAR
   50 
   51 $BBOLD A. $EBOLD
   52 Find an expression for the number of bacteria after \(t\) hours.$BR
   53 \{ans_rule(60)\}
   54 $PAR
   55 
   56 $BBOLD B. $EBOLD
   57 Find the number of bacteria after \{$t1 + 1\} hours.$BR
   58 \{ans_rule(30)\}
   59 $PAR
   60 
   61 $BBOLD C. $EBOLD
   62 Find the growth rate after \{$t1 + 1\} hours.$BR
   63 \{ans_rule(30)\}
   64 $PAR
   65 
   66 $BBOLD D. $EBOLD
   67 After how many hours will the population reach 30000?$BR
   68 \{ans_rule(30)\}
   69 $PAR
   70 
   71 $PAR
   72 END_TEXT
   73 $k = log($later/$initial)/$t1;
   74 ANS(fun_cmp("$initial*exp($k*t)", var=>['t']));
   75 ANS(num_cmp($initial*exp($k*($t1+1)), tol=>2));
   76 ANS(num_cmp($initial*exp($k*($t1+1))*$k, tol=>2));
   77 ANS(num_cmp(log(30000/$initial)/$k, tol=>2));
   78 
   79 ENDDOCUMENT();
   80 
   81 
   82 
   83