View of /trunk/NationalProblemLibrary/Rochester/setAlgebra28ExpFunctions/sw6_2_17.pg

    1 #DESCRIPTION
    2 ##  Algebra problem: Natural Exponential Functions
    3 ##ENDDESCRIPTION
    4 
    5 ##KEYWORDS('algebra', 'natural exponential function')
    6 ## tsch tagged and PAID on 12-12-2003
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Exponential and Logarithmic Functions')
   10 ## DBsection('The Natural Exponential Function')
   11 ## Date('6/3/2002')
   12 ## Author('')
   13 ## Institution('')
   14 ## TitleText1('College Algebra')
   15 ## EditionText1('3')
   16 ## AuthorText1('Stewart, Redlin, Watson')
   17 ## Section1('6.2')
   18 ## Problem1('17')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   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 $p=random(900,1000,5);
   34 $a=random(10,50,5);
   35 $r=$a/100;
   36 
   37 BEGIN_TEXT
   38 The number of bacteria in a culture is given by the function
   39 \[
   40 n(t)=$p e^{$r t}
   41 \]
   42 where \(t\) is measured in hours.
   43 $BR
   44 (a) What is the relative rate of growth of this bacterium population?
   45 $BR
   46 Your answer is \{ans_rule(10) \} percent
   47 $BR
   48 (b) What is the initial population of the culture (at t=0)?
   49 $BR
   50 Your answer is \{ans_rule(15) \}
   51 $BR
   52 (c) How many bacteria will the culture contain at time t=5?
   53 $BR
   54 Your answer is \{ans_rule(15) \}
   55 $BR
   56 END_TEXT
   57 
   58 $ans1 = $a;
   59 $ans2 = $p;
   60 $ans3 = $p*exp($r*5);
   61 
   62 ANS(num_cmp($ans1));
   63 ANS(num_cmp($ans2));
   64 ANS(num_cmp($ans3));
   65 
   66 ENDDOCUMENT();        # This should be the last executable line in the problem.