TT2YF11SOLN - MATH 1080 TERM TEST 2 SOLUTIONS YELLOW PAGE 1...

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MATH 1080 TERM TEST 2 SOLUTIONS YELLOW PAGE 1 Page 1 PART I Each question in this part has exactly one correct answer. Remember CIRCLE your answer on this questionnaire and clearly indicate your answer on the computer score card. 1. If the size of a certain population at generation is given by 8 œ "!" 62 TÐ"!"Ñ œ "!!!  Ð  8Ñ 8œ" "!! then the numerical value of is TÐ"!"Ñ (A) (B) (C) (E) ""ß %!! ""ß &!! ""ß '!! ""ß (!! ""ß )!! (D) SOLUTION T Ð"!"Ñ œ "!!!  Ð'  #8Ñ œ "!!!  '  # 8 œ "!!!  'Ð"!!Ñ  # "!! "!! "!! Ð"!!ÑÐ"!"Ñ #  T Ð"!"Ñ œ "!!!  '!!  "!"!! œ ""ß (!! (D) 2. In an experiment, the residual amount of a drug in the patient's system at the end of the th dosage period was found to be ( ) . Then (30) 8V Ð 8 Ñ œ ) / V œ 8 3 3œ" !Þ' (A) (B) ( ) (C) ( ) )) // "Ð/ Ñ Ñ Ñ "/ 8  !Þ' $! !Þ' !Þ' $" !Þ' !Þ' !Þ' !Þ' !Þ' ( ) (E) (D) )/ Ñ !Þ' !Þ' !Þ' !Þ' !Þ' 30 SOLUTION () ) VÐ$!Ñ œ ) / œ Ð)/ / œ ) / $! $! 33 " Ñ 3œ" 3œ" !Þ' $! !Þ' !Þ' !Þ' !Þ' !Þ' (D) 3. lim equals Bp% ""#B  $ %B (A) + (B) (D) (E) 1 1 # # $$ $ $  (C) SOLUTION Bp% Bp% ""  #B  $ ""  #B  $ ""  #B  $ œ ""  #B  $  ! ! œœ Bp% Bp% ""  #B $ %BÑÐ ""#B  $ Ñ Ñ "" #B  $ ## ÐÐ $ Bp% Bp% )#B Ð%BÑÐ #Ð% BÑ " " Ð (C) œ Bp% " ""  #B  $ Bp$ #$ $
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MATH 1080 TERM TEST 2 SOLUTIONS YELLOW PAGE 2 Page 2 4. If X = X X , where X = and X = then X equals ? 88 $ 8 " ' 8" 0 13 (A) (B) (D) (E) (' () )! )# )% (C) SOLUTION ? = X X = X 8 8 Ê % 8 8" 8" 8" f o r = X X 8 œ " À %  " œ %Ð'Ñ  " œ #$ #" ! f o r X 8 œ # À %  # œ %Ð#$Ñ  #Ð'Ñ œ )! $# " (C) 5. The strictly positive equilibriums for the difference equation = ( ) ( ) are 1 \\ " " \ 8" #% 2 (A) and and (C) and (D) and (E) and #) $) %( %' # (B) SOLUTION = ( ) ( = ( ) ( 11 \ \ ""  \ Ñ Ê \ \ ""  \ Ñ 8" #% #% II I ## Ê #%\ "" \  Ð\ Ñ Ê Ð\ Ñ  "" \  #%\ œ ! I I I I = () $$ Ê\ ÐÐ\ Ñ ""\ #%Ñœ! Ê\ Ð\ $ÑÐ\ )Ñœ! I I I I # Ê\ œ$ \ œ) and (strictly positive) (B) 6. For a difference equation X X you are given the graph of 8" œ0Ð Ñ ß 8 X X X . ? 8 Ñ If X , then the value of X is a number that is strictly between "# œ* "% (A) and 1 (B) 1 and 1 (C) 1 and (D) and (E) and "% ' ') )# ! "# "% "! "# ? X 8 o\ # p ? ? "# "$ =4 X 8 SOLUTION X X X X X X "$ "# œ Ê œ œ * % œ " $ ?? Then X X X 1 "% œ " $ # œ & "$ "$ ? (A)
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MATH 1080 TERM TEST 2 SOLUTIONS YELLOW PAGE 3 Page 3 7. If the solution of the difference equation X X is X then 8" œ +  , œ %!!  $!!Ð Ñ 88 $ % 8 the parameters and , the initial population X , and the steady state X = lim X are +, !
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TT2YF11SOLN - MATH 1080 TERM TEST 2 SOLUTIONS YELLOW PAGE 1...

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