View of /trunk/NationalProblemLibrary/NAU/setExpLog/WPExp2.pg

    1 ##DESCRIPTION
    2 ## DBsubject('Algebra')
    3 ## DBchapter('Exponential and Logarithmic Functions')
    4 ## DBsection('Exponential and Logarithmic Equations')
    5 ## KEYWORDS('word problem')
    6 ## Author('Katie Louchart')
    7 ## Institution('NAU')
    8 ##ENDDESCRIPTION
    9 
   10 # File Created: 8/9/05
   11 # Location: Northern Arizona University
   12 # Course: Precalculus
   13 
   14 DOCUMENT();
   15 
   16 loadMacros(
   17 "PG.pl",
   18 "PGbasicmacros.pl",
   19 "PGchoicemacros.pl",
   20 "PGanswermacros.pl",
   21 "PGauxiliaryFunctions.pl",
   22 "PGasu.pl",
   23 "extraAnswerEvaluators.pl"
   24 );
   25 
   26 TEXT(beginproblem());
   27 $showPartialCorrectAnswers = 1;
   28 
   29 
   30 $a=random(3,6, .01);
   31 $b=random(35,75,5);
   32 $c=$a/100;
   33 $ans=log($b/100)/(-$c);
   34 
   35 BEGIN_TEXT
   36 In a certain country, the rate of deforestation is about $a$PERCENT per year.  Assume that the amount of forest remaining is given by the function
   37 $PAR
   38 \( F = F_0 e^{-$c t} \)
   39 $BR
   40 $BR
   41 where \( F_0 \) is the present acreage of forest land and \( t \) is the time in years from the present.  In how many years will there be only $b$PERCENT  of the present acreage remaining?
   42 $BR
   43 Round your answer to three decimal places.
   44 $PAR
   45 \{ans_rule(20) \} years from now
   46 END_TEXT
   47 
   48 
   49 ANS(num_cmp($ans));
   50 
   51 
   52 ENDDOCUMENT();        # This should be the last executable line in the problem.