qu.1.topic=Difference Equations@

qu.1.1.mode=Inline@
qu.1.1.name=X_n+2=X_n+1+x_n@
qu.1.1.comment=@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$a=['1','2','3'];
$b=['4','5','6','7','8'];
$c=rint(2,5);
$d=rint(5,7);
$picka=switch(rint(3),$a);
$pickb=switch(rint(5),$b);
$ANS = maple("
myProc := proc(n)
 option remember:
 if n=0 then $picka:
 elif n=1 then $pickb:
 else thisproc(n-1) + $c*thisproc(n-2):
 end if:
end proc:
myProc($d)
");@
qu.1.1.uid=8515b8c0-1a92-48e5-baa1-4add3deab2db@
qu.1.1.info=  Author=Steve Crane, Gord Clement;
  Course=Introductory Calculus for the Biological Sciences;
  Topic=Difference Equations;
  Sub-Topic=Second Order;
@
qu.1.1.weighting=1@
qu.1.1.numbering=alpha@
qu.1.1.part.1.name=sro_id_1@
qu.1.1.part.1.maple_answer=$ANS@
qu.1.1.part.1.editing=useHTML@
qu.1.1.part.1.question=(Unset)@
qu.1.1.part.1.libname=@
qu.1.1.part.1.mode=Maple@
qu.1.1.part.1.allow2d=1@
qu.1.1.part.1.plot=@
qu.1.1.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.1.part.1.type=formula@
qu.1.1.question=<p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>2</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>X</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>$c</mi><mo lspace='0.0em' rspace='0.0em'>&sdot;</mo><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mstyle></math>, where <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$picka</mi></mrow></mstyle></math> and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi>$pickb</mi></mrow></mstyle></math> then&nbsp;<math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>$d</mi></mrow></msub></mrow></mstyle></math> equals</p><p>&nbsp;</p><p><1><span>&nbsp;</span></p>@

qu.1.2.mode=Inline@
qu.1.2.name=Insecticide Testing@
qu.1.2.comment=@
qu.1.2.editing=useHTML@
qu.1.2.solution=@
qu.1.2.algorithm=$a=['5','10','15','20'];
$picka=switch(rint(4),$a);
$ra=0.01*$picka;
$b=['20','25','30'];
$pickb=switch(rint(3),$b);
condition: ne($picka,$pickb);
$rb=0.01*$pickb;
$c=['50','55','60','65','70'];
$pickc=switch(rint(5),$c);
$ANS="x+$ra*x-$rb*(x+$ra*x)-$pickc";@
qu.1.2.uid=a346699e-1a00-470a-84b9-0b87ffc57e40@
qu.1.2.info=  Author=Steve Crane, Gord Clement;
  Course=Introductory Calculus for the Biological Sciences;
  Topic=Difference Equations;
  Sub-Topic=Application;
@
qu.1.2.weighting=1@
qu.1.2.numbering=alpha@
qu.1.2.part.1.name=sro_id_1@
qu.1.2.part.1.maple_answer=$ANS@
qu.1.2.part.1.editing=useHTML@
qu.1.2.part.1.question=(Unset)@
qu.1.2.part.1.libname=@
qu.1.2.part.1.mode=Maple@
qu.1.2.part.1.allow2d=1@
qu.1.2.part.1.plot=@
qu.1.2.part.1.maple=is(abs(($ANSWER)-($RESPONSE)) < 0.1);@
qu.1.2.part.1.type=formula@
qu.1.2.question=<p>In an insecticide testing experiment on controlling the population of insects it was observed that each month there was a $picka% increasein the insect population.&nbsp; After this increase, the insecticide was applied resulting in a $pickb% decrease in the population.&nbsp; After the decrease $pickc insects were removed for testing.&nbsp;</p><p>State the difference equation represeing the chance in size of the insect population at the end of each month.</p><p>Note: Use "x" to represent <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>x</mi><mrow><mi>n</mi></mrow></msub></mrow></mstyle></math>.</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p>@

qu.1.3.mode=Inline@
qu.1.3.name=General solution - Difference Equations@
qu.1.3.comment=<p>Recall: if the Model is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>b</mi></mrow></mstyle></math> then the general solution is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>nb</mi></mrow></mstyle></math></p>@
qu.1.3.editing=useHTML@
qu.1.3.solution=@
qu.1.3.algorithm=$a=['100','200','300','400','500'];
$picka=switch(rint(5),$a);
$b=['2','5','8','10'];
$pickb=switch(rint(4),$b);
$c=['5','10','15','20','25','30','35'];
$pickc=switch(rint(7),$c);
$f="x->$picka+$pickb*x";@
qu.1.3.uid=491ea1cb-46ac-4406-a7cb-d83698775d68@
qu.1.3.weighting=1@
qu.1.3.numbering=alpha@
qu.1.3.part.1.name=sro_id_1@
qu.1.3.part.1.maple_answer=($f)($pickc)@
qu.1.3.part.1.editing=useHTML@
qu.1.3.part.1.question=(Unset)@
qu.1.3.part.1.libname=@
qu.1.3.part.1.mode=Maple@
qu.1.3.part.1.allow2d=1@
qu.1.3.part.1.plot=@
qu.1.3.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.3.part.1.type=formula@
qu.1.3.question=<p>Determine the general solutions of the first order difference equations and the term <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>$pickc</mi></mrow></msub></mrow></mstyle></math>.</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>&Delta;X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$pickb and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$picka</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p>@

qu.1.4.mode=Inline@
qu.1.4.name=Steady State ii@
qu.1.4.comment=<p>Recall: if the model is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>aX</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>b</mi></mrow></mstyle></math> then the general solution is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfenced open='(' close=')' separators=','><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac></mrow></mfenced><msup><mi>a</mi><mrow><mi>n</mi></mrow></msup></mrow></mstyle></math>.&nbsp; Then the steady state <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>X</mi></mrow><mrow><mi>__</mi></mrow></mover></mrow></mstyle></math>equals</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>X</mi></mrow><mi>&macr;</mi></mover></mrow></mstyle></math> = <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>n</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></munder><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>n</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></munder><mfenced open='(' close=')' separators=','><mrow><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='(' close=')' separators=','><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac></mrow></mfenced><msup><mi>a</mi><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math></p>
<p>&nbsp;</p>@
qu.1.4.editing=useHTML@
qu.1.4.solution=@
qu.1.4.algorithm=$a=rint(2,5);
$b=['500','1000','1500','2000','2500','-2000','-1500','-500'];
$pickb=switch(rint(8),$b);
$c=['100','200','300','400','500'];
$pickc=switch(rint(5),$c);
$func="$pickb+($pickc)*   ($a)^x";
$disp=maple("printf(MathML[ExportPresentation]($func))");@
qu.1.4.uid=e28756b3-25e0-4e00-b352-fe30d137f233@
qu.1.4.weighting=1@
qu.1.4.numbering=alpha@
qu.1.4.part.1.name=sro_id_1@
qu.1.4.part.1.maple_answer=inf@
qu.1.4.part.1.editing=useHTML@
qu.1.4.part.1.question=(Unset)@
qu.1.4.part.1.libname=@
qu.1.4.part.1.mode=Maple@
qu.1.4.part.1.allow2d=0@
qu.1.4.part.1.plot=@
qu.1.4.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.4.part.1.type=maple@
qu.1.4.question=<p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mstyle></math>= $disp then determine the steady state <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>X</mi></mrow><mi>&macr;</mi></mover></mrow></mstyle></math>.</p><p>Note: Enter "inf" for infinity and "D.N.E." for "Does Not Exist".</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p>@

qu.1.5.mode=Inline@
qu.1.5.name=Steady State@
qu.1.5.comment=<p>Recall: if the Model is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>aX</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>b</mi></mrow></mstyle></math> then the general solution is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfenced open='(' close=')' separators=','><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac></mrow></mfenced><msup><mi>a</mi><mrow><mi>n</mi></mrow></msup></mrow></mstyle></math>.&nbsp; Then the steady state <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>X</mi></mrow><mrow><mi>__</mi></mrow></mover></mrow></mstyle></math>equals</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>X</mi></mrow><mi>&macr;</mi></mover></mrow></mstyle></math> = <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>n</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></munder><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><munder><mo lspace='0.0em' rspace='0.1666667em' movablelimits='true'>lim</mo><mrow><mi>n</mi><mo mathvariant='italic' lspace='0.2777778em' rspace='0.2777778em' stretchy='true'>&rightarrow;</mo><mo mathvariant='italic' lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo mathvariant='italic' lspace='0.0em' rspace='0.0em'>&infin;</mo></mrow></munder><mfenced open='(' close=')' separators=','><mrow><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mfenced open='(' close=')' separators=','><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac></mrow></mfenced><msup><mi>a</mi><mrow><mi>n</mi></mrow></msup></mrow></mfenced></mrow></mstyle></math></p>
<p>&nbsp;</p>@
qu.1.5.editing=useHTML@
qu.1.5.solution=@
qu.1.5.algorithm=$a=rint(1,3);
$b=['500','1000','1500','2000','2500'];
$pickb=switch(rint(5),$b);
$c=['100','200','300','400','500'];
$pickc=switch(rint(5),$c);
$func="$pickb+$pickc*($a/3)^x";
$disp=maple("MathML[ExportPresentation]($func)");@
qu.1.5.uid=445a3dc6-691a-41ed-bb6e-c86f8826daa5@
qu.1.5.weighting=1@
qu.1.5.numbering=alpha@
qu.1.5.part.1.name=sro_id_1@
qu.1.5.part.1.maple_answer=$pickb@
qu.1.5.part.1.editing=useHTML@
qu.1.5.part.1.question=(Unset)@
qu.1.5.part.1.libname=@
qu.1.5.part.1.mode=Maple@
qu.1.5.part.1.allow2d=1@
qu.1.5.part.1.plot=@
qu.1.5.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.5.part.1.type=formula@
qu.1.5.question=<p>If <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mstyle></math>=$disp then determine the steady state <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mover><mrow><mi>X</mi></mrow><mi>&macr;</mi></mover></mrow></mstyle></math>.</p><p>Note: Enter "inf" for <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><mi>&infin;</mi></mrow></mstyle></math>and "D.N.E." for "Does Not Exist".</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p>@

qu.1.6.mode=Inline@
qu.1.6.name=General solution - Difference Equations ii@
qu.1.6.comment=<p>Recall: if the Model is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><msub><mi>aX</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi>b</mi></mrow></mstyle></math> then the general solution is <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mfenced open='(' close=')' separators=','><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mfrac><mi>b</mi><mrow><mn>1</mn><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><mi>a</mi></mrow></mfrac></mrow></mfenced><msup><mi>a</mi><mrow><mi>n</mi></mrow></msup></mrow></mstyle></math>.</p>@
qu.1.6.editing=useHTML@
qu.1.6.solution=@
qu.1.6.algorithm=$a=['500','1000','1500','2000'];
$picka=switch(rint(4),$a);
$b=['100','200','300','400','500'];
$pickb=switch(rint(5),$b);
$c=['5','10','15','20','25','30','35'];
$pickc=switch(rint(7),$c);
$d=range(-3,-2);
$e=$d+5;
condition: ne($picka,$pickb/((5-$e)/5));
$f="x->($e/5)*x+$pickb";
$g="x->$pickb/((5-$e)/5)+($picka-$pickb/((5-$e)/5))*($e/5)^x";
$df=maple("
g:= $g:
MathML[ExportPresentation](g(x))");@
qu.1.6.uid=a146e59f-3344-43ab-81a9-7a3442e0c1b7@
qu.1.6.weighting=1@
qu.1.6.numbering=alpha@
qu.1.6.part.1.name=sro_id_1@
qu.1.6.part.1.maple_answer=($f)($pickc)@
qu.1.6.part.1.editing=useHTML@
qu.1.6.part.1.question=(Unset)@
qu.1.6.part.1.libname=@
qu.1.6.part.1.mode=Maple@
qu.1.6.part.1.allow2d=1@
qu.1.6.part.1.plot=@
qu.1.6.part.1.maple=is(($ANSWER)-($RESPONSE) = 0);@
qu.1.6.part.1.type=formula@
qu.1.6.question=<p>Determine the term <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>$pickc</mi></mrow></msub></mrow></mstyle></math>&nbsp;for&nbsp;the first order difference equation, specified below.</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>&Delta;X</mi><mrow><mi>n</mi></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$pickb and <math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mn>0</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo></mrow></mstyle></math>$picka</p><p><span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p>@

qu.1.7.mode=Inline@
qu.1.7.name=Equilibrium@
qu.1.7.comment=@
qu.1.7.editing=useHTML@
qu.1.7.solution=@
qu.1.7.algorithm=$a=rint(2,7);
$b=rint(2,10);
condition: ne($a,$b);
$func="(x*($b-x)/$a)-x";
$ANS=maple("solve($func=0)");
$ANS1=switch(0,$ANS);
$ANS2=switch(1,$ANS);@
qu.1.7.uid=9f4c111c-e9e2-4eed-96a9-cc785cd120f3@
qu.1.7.weighting=1,1@
qu.1.7.numbering=alpha@
qu.1.7.part.1.name=sro_id_1@
qu.1.7.part.1.maple_answer=$ANS1 @
qu.1.7.part.1.editing=useHTML@
qu.1.7.part.1.question=(Unset)@
qu.1.7.part.1.libname=@
qu.1.7.part.1.mode=Maple@
qu.1.7.part.1.allow2d=1@
qu.1.7.part.1.plot=@
qu.1.7.part.1.maple= grade:=0.0:
 if(is(($RESPONSE)-($ANS2) = 0)) then grade:=1.0:
 elif(simplify($ANS1-$RESPONSE)=0) then grade:=1.0: 
 end if:
 grade;@
qu.1.7.part.1.type=formula@
qu.1.7.part.2.name=sro_id_2@
qu.1.7.part.2.maple_answer=$ANS2@
qu.1.7.part.2.editing=useHTML@
qu.1.7.part.2.question=(Unset)@
qu.1.7.part.2.libname=@
qu.1.7.part.2.mode=Maple@
qu.1.7.part.2.allow2d=1@
qu.1.7.part.2.plot=@
qu.1.7.part.2.maple= grade:=0.0:
 if(is(($RESPONSE)-($ANS2) = 0)) then grade:=1.0:
 elif(simplify($ANS1-$RESPONSE)=0) then grade:=1.0: 
 end if:
 grade;@
qu.1.7.part.2.type=formula@
qu.1.7.question=<p>Find the equilibrium values for the following difference equation:</p><p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000' veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>X</mi><mrow><mi>n</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mn>1</mn><mrow><mi>$a</mi></mrow></mfrac><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub><mfenced open='(' close=')' separators=','><mrow><mi>$b</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&minus;</mo><msub><mi>X</mi><mrow><mi>n</mi></mrow></msub></mrow></mfenced></mrow></mstyle></math></p><p><br /><span>&nbsp;</span><1><span>&nbsp;</span></p><p>&nbsp;</p><p><span><span>&nbsp;</span><2><span>&nbsp;</span></span></p><p>&nbsp;</p>@

