WeBWorK_ProgrammingExercises/While2.pg at master · esullivanmath/WeBWorK_ProgrammingExercises · GitHub

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##DESCRIPTION
##  This problem is meant to have students write brief pieces of code to solve problems that have a specific numerical answer.
##ENDDESCRIPTION

##KEYWORDS('programming', 'code')

## DBsubject('Programming')
## DBchapter('')
## DBsection('')
## Date('6/7/2016')
## Author('')
## Institution('')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

########################################################################

DOCUMENT();
loadMacros(
"PG.pl",
"PGauxiliaryFunctions.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"MathObjects.pl",
"problemRandomize.pl",
"PGanswermacros.pl",
"PGgraphmacros.pl",
"PGnumericalmacros.pl",
"PGstatisticsmacros.pl",
"answerHints.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;
# How many attempts before a hint?
$showHint = 10;

#Allow the student to generate a new (re-randomized) problem
#AFTER they have submitted a correct answer.
ProblemRandomize(onlyAfterDue=>0);
##############################################################


$N = random(15000,17000,1);
$a = random(0.8,0.9,0.1);
$Neq = random(1,100);
$b = $Neq * ( 1 - $a);
$N1 = $N*$a+$b;
$N2 = $N1*$a+$b;

$per = random(1.1,4.9,.1);
$x = random(1,25);

$val = $N;

while (abs($val-$Neq) > $x){
$val = $a*$val + $b;
}


##############################################################
#
#  Text
#
#

Context()->texStrings;
BEGIN_TEXT
Consider a mathematical process where we take a number, multiply it by a constant, and then add another constant.  For example, if we start with the number 500, multiply it by 1/2, then add 7, we have 257.  If again we multiply by 1/2, then add 7, we have 135.5.  If again we multiply by 1/2, then add 7, we have 74.75.
$PAR
Write MATLAB program that starts with the number $N, multiplies this by $a, then adds $b.  If we do this once, we get $N1.  If we do this again, we get $N2.  Have your program continue this process until we have a number that is within $x of $Neq.  What number do we end up with?  In other words, if we continue multiplying by $a and adding $b, what is the first number that we get which is less than $x away from $Neq?
$PAR
\{ans_rule(15)\}
$PAR


END_TEXT
BEGIN_HINT
To solve this problem you will likely need a "while-loop" which checks whether the difference between our current value and $Neq is larger than $x.
$BR
END_HINT
ANS(num_cmp($val,tol=>.01));

##############################################################
#
#  Answers
#
#


ENDDOCUMENT();