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ColorFunction->RGBColor], BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True], Selectable->False], DefaultBaseStyle->"ImageGraphics", ImageSize->{478.0390625, Automatic}, ImageSizeRaw->{960, 640}, PlotRange->{{0, 960}, {0, 640}}]],ExpressionUUID->"742f4a33-9e53-4e0a-82b6-3b93566ed8c1"]], "Text", CellChangeTimes->{{3.744611228741395*^9, 3.744611237300206*^9}, { 3.744611834947447*^9, 3.7446118349475718`*^9}, {3.744611894220317*^9, 3.744611894222801*^9}}, TextAlignment->Center,ExpressionUUID->"d5f87d81-b261-429b-a96d-5354c78e67e9"], Cell["\<\ The common myna bird was introduced into Australia in order to control \ insects affecting market gardens in Melbourne. It is now considered to be \ one Australia\[CloseCurlyQuote]s problem pests due to its negative impact on \ native birds through competition for food, nesting sites and territories. In 1976, the species was introduced to an urban area in New South Wales. By \ 1991 the area averaged 15 birds per square kilometre and by 1994 the density \ reached an average of 75 birds per square kilometre. A model for the increasing density of the myna bird population is thought to \ be \ \>", "Text", CellChangeTimes->{{3.744611492879828*^9, 3.744611601309266*^9}, { 3.7446119021672564`*^9, 3.744611970218684*^9}, {3.744612044790051*^9, 3.744612170187063*^9}, {3.744612503848124*^9, 3.7446126057780657`*^9}},ExpressionUUID->"576b8e3e-9ae5-452d-ad25-\ 6887dd7bcb81"], Cell[TextData[Cell[BoxData[ FormBox[ RowBox[{"D", "=", RowBox[{ SubscriptBox["D", "0"], "\[Times]", SuperscriptBox["10", RowBox[{"k", " ", "t"}]]}]}], TraditionalForm]], FormatType-> "TraditionalForm",ExpressionUUID->"1c7a8fd5-b861-4084-a13f-14f040ca9078"]], \ "Text", CellChangeTimes->{{3.74461261324035*^9, 3.744612638063306*^9}}, TextAlignment->Center,ExpressionUUID->"105b03d4-40d5-407a-a8ee-ee50f6a88a6c"], Cell[BoxData[ RowBox[{ RowBox[{"A", "[", "t_", "]"}], ":=", RowBox[{"0.005", "*", SuperscriptBox["10", RowBox[{"0.233", "*", "t"}]]}]}]], "Input", CellChangeTimes->{{3.745544611748806*^9, 3.745544657618307*^9}, { 3.74556922089083*^9, 3.745569230753706*^9}, {3.745569550754135*^9, 3.745569586955226*^9}}, CellLabel-> "In[140]:=",ExpressionUUID->"5fbfcdc7-aedf-44ce-a14c-ac8ce3be365c"], Cell[TextData[{ "where D is the average density of the bird per square kilometre t years \ after 1976 and ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["D", "0"], " ", "and", " ", "k"}], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "f096b726-2e7a-4b26-aca4-a7befdf4dad6"], " are constants.\n\na) Show that ", Cell[BoxData[ FormBox[ RowBox[{"k", "=", "0.233"}], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "b3c67100-84ae-48b9-b01f-f15ecfcd3904"], " and ", Cell[BoxData[ FormBox[ SubscriptBox["D", "0"], TraditionalForm]],ExpressionUUID-> "6727a527-b36f-44fd-b334-eab65ca619ab"], "= 0.005." }], "Text", CellChangeTimes->{{3.7446126475582657`*^9, 3.7446126811079407`*^9}, { 3.7446131724302053`*^9, 3.7446132851931868`*^9}},ExpressionUUID->"35a005ce-af2d-43d7-be35-\ 0ce5d787a1e5"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"A", "[", "15", "]"}], "\[Equal]", "15"}], ",", " ", RowBox[{ RowBox[{"A", "[", "18", "]"}], "\[Equal]", "75"}]}], "}"}], ",", RowBox[{"{", RowBox[{"k", ",", "a"}], "}"}], ",", " ", "Reals"}], "]"}], "//", "N"}]], "Input", CellChangeTimes->{{3.744613286829316*^9, 3.744613287221834*^9}, { 3.745565029187313*^9, 3.745565035671859*^9}, {3.745569021017205*^9, 3.7455690269331017`*^9}, {3.745569066829598*^9, 3.745569143931744*^9}}, CellLabel-> "In[129]:=",ExpressionUUID->"74043784-264c-42db-8094-2f7bf9a38710"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ RowBox[{"k", "\[Rule]", "0.23299000144533957`"}], ",", RowBox[{"a", "\[Rule]", "0.0048`"}]}], "}"}], "}"}]], "Output", CellChangeTimes->{{3.7455691090250797`*^9, 3.7455691447691927`*^9}}, CellLabel-> "Out[129]=",ExpressionUUID->"5478ea3b-d16b-40d1-9e79-5a186f701773"] }, Open ]], Cell["\<\ Answer\ \>", "Text", CellChangeTimes->{{3.742498818130303*^9, 3.742498832880702*^9}},ExpressionUUID->"2a7f76a1-75f1-4e43-97de-\ 4aeca78fc0ce"], Cell["Assume a = D(0)", "Text", CellChangeTimes->{{3.745569162228612*^9, 3.7455691766792707`*^9}}, Background->RGBColor[ 1, 0.85, 0.85],ExpressionUUID->"fd29a2fe-f09c-4a80-b84d-3ce45b091c68"], Cell["\<\ b) A \[OpenCurlyDoubleQuote]project\[CloseCurlyDoubleQuote] was introduced \ in 1996 to curb the growth in numbers of these birds. What does the model \ predict was the average density of the myna bird population at the time the \ project was introduced in 1996.\ \>", "Text", CellChangeTimes->{{3.744613481924079*^9, 3.7446134831910152`*^9}, { 3.7446144850695972`*^9, 3.7446146105969887`*^9}},ExpressionUUID->"0bdfd091-188e-4c67-aea9-\ 1bb94ed451d5"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"A", "[", "20", "]"}]], "Input", CellChangeTimes->{{3.7446146124228354`*^9, 3.744614612796564*^9}, { 3.745569205181263*^9, 3.745569206944425*^9}}, CellLabel-> "In[141]:=",ExpressionUUID->"b14514c5-4889-4ade-870f-f993f153a61b"], Cell[BoxData["228.54409480743757`"], "Output", CellChangeTimes->{3.745569207578917*^9, 3.745569237934021*^9, 3.7455695582446413`*^9, 3.745569593342671*^9}, CellLabel-> "Out[141]=",ExpressionUUID->"c349c28b-c873-4066-9e70-be7889d71c1e"] }, Open ]], Cell["\<\ Answer\ \>", "Text", CellChangeTimes->{{3.742498818130303*^9, 3.742498832880702*^9}},ExpressionUUID->"6fd9af48-667f-465d-b99d-\ 3d3cb9f71258"], Cell["229 birds per square kilometre ", "Text", CellChangeTimes->{{3.745569254562079*^9, 3.745569263366558*^9}, { 3.745569605693412*^9, 3.745569606303932*^9}}, Background->RGBColor[ 1, 0.85, 0.85],ExpressionUUID->"4008be7e-40fa-40f2-a8fe-9afcdc27cbc9"], Cell[TextData[{ "\nc) Sometime after the project is successfully implemented, a different \ model for the average density of the bird population becomes applicable. \ This model is given by ", Cell[BoxData[ FormBox[ RowBox[{"D", "=", RowBox[{ RowBox[{"30", "\[Times]", SuperscriptBox["10", RowBox[{"-", FractionBox["t", "3"]}]]}], "+", RowBox[{"b", "."}]}]}], TraditionalForm]], FormatType->"TraditionalForm",ExpressionUUID-> "1f8fc595-116f-414e-a7c2-f5912a201bb0"], " Four years later, the average density is reduced to 40 birds per square \ kilometre. How much can the average density expect to be reduced?" }], "Text", CellChangeTimes->{{3.744614651744629*^9, 3.7446147714887*^9}},ExpressionUUID->"ebd0aeae-868c-487e-9e33-d91fc7f5d738"], Cell[BoxData[ RowBox[{ RowBox[{"f", "[", "t_", "]"}], ":=", RowBox[{ RowBox[{"30", "*", SuperscriptBox["10", RowBox[{"-", FractionBox["t", "3"]}]]}], "+", "b"}]}]], "Input", CellChangeTimes->{{3.7455692979701557`*^9, 3.74556934832782*^9}}, CellLabel-> "In[135]:=",ExpressionUUID->"7b98161c-39b7-4c37-96f8-5e741d084b35"], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{"Solve", "[", RowBox[{ RowBox[{ RowBox[{"f", "[", "4", "]"}], "\[Equal]", "40"}], ",", "b"}], "]"}], "//", "N"}]], "Input", CellChangeTimes->{{3.744614776075326*^9, 3.744614776626593*^9}, { 3.745569364120912*^9, 3.745569382556787*^9}}, CellLabel-> "In[137]:=",ExpressionUUID->"e6db590d-e675-46ce-9849-a3d149f3dbf7"], Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{"b", "\[Rule]", "38.607523349916164`"}], "}"}], "}"}]], "Output", CellChangeTimes->{{3.745569379687508*^9, 3.745569383302837*^9}}, CellLabel-> "Out[137]=",ExpressionUUID->"c082a2a7-06a9-49b2-b07d-4c50d03795a7"] }, Open ]], Cell["\<\ Answer\ \>", "Text", CellChangeTimes->{{3.742498818130303*^9, 3.742498832880702*^9}},ExpressionUUID->"41edb4b6-3097-48d3-a8aa-\ 576d0b2b27f7"], Cell["\<\ The average density can be expected to be reduced close to 39 birds per \ square kilometre. b is approximately 39 which is the asymptote. \ \>", "Text", CellChangeTimes->{{3.745569413664351*^9, 3.745569443325431*^9}, { 3.745569634331359*^9, 3.7455696562414207`*^9}}, Background->RGBColor[ 1, 0.85, 0.85],ExpressionUUID->"afa89ba1-140e-41d1-aa8b-4c4c34f340f7"], Cell["", "Text",ExpressionUUID->"a5f40b10-2398-44c7-89d6-5f53beda8f95"] }, Open ]] }, ScreenStyleEnvironment->"SlideShow", WindowSize->{1065, 604}, WindowMargins->{{Automatic, 162}, {Automatic, 25}}, FrontEndVersion->"11.3 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 5, \ 2018)", StyleDefinitions->FrontEnd`FileName[{"Report"}, "StandardReport.nb", CharacterEncoding -> "UTF-8"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 345, 4, 255, "Title",ExpressionUUID->"204be495-b38c-4093-af17-4105cfcc7706"], Cell[928, 28, 1826784, 29952, 339, "Text",ExpressionUUID->"d5f87d81-b261-429b-a96d-5354c78e67e9"], Cell[1827715, 29982, 897, 17, 375, "Text",ExpressionUUID->"576b8e3e-9ae5-452d-ad25-6887dd7bcb81"], Cell[1828615, 30001, 437, 11, 51, "Text",ExpressionUUID->"105b03d4-40d5-407a-a8ee-ee50f6a88a6c"], Cell[1829055, 30014, 407, 10, 59, "Input",ExpressionUUID->"5fbfcdc7-aedf-44ce-a14c-ac8ce3be365c"], Cell[1829465, 30026, 865, 25, 159, "Text",ExpressionUUID->"35a005ce-af2d-43d7-be35-0ce5d787a1e5"], Cell[CellGroupData[{ Cell[1830355, 30055, 668, 17, 59, "Input",ExpressionUUID->"74043784-264c-42db-8094-2f7bf9a38710"], Cell[1831026, 30074, 337, 8, 59, "Output",ExpressionUUID->"5478ea3b-d16b-40d1-9e79-5a186f701773"] }, Open ]], Cell[1831378, 30085, 157, 6, 87, "Text",ExpressionUUID->"2a7f76a1-75f1-4e43-97de-4aeca78fc0ce"], Cell[1831538, 30093, 195, 3, 67, "Text",ExpressionUUID->"fd29a2fe-f09c-4a80-b84d-3ce45b091c68"], Cell[1831736, 30098, 470, 10, 159, "Text",ExpressionUUID->"0bdfd091-188e-4c67-aea9-1bb94ed451d5"], Cell[CellGroupData[{ Cell[1832231, 30112, 255, 5, 59, "Input",ExpressionUUID->"b14514c5-4889-4ade-870f-f993f153a61b"], Cell[1832489, 30119, 242, 4, 59, "Output",ExpressionUUID->"c349c28b-c873-4066-9e70-be7889d71c1e"] }, Open ]], Cell[1832746, 30126, 157, 6, 87, "Text",ExpressionUUID->"6fd9af48-667f-465d-b99d-3d3cb9f71258"], Cell[1832906, 30134, 258, 4, 67, "Text",ExpressionUUID->"4008be7e-40fa-40f2-a8fe-9afcdc27cbc9"], Cell[1833167, 30140, 799, 19, 202, "Text",ExpressionUUID->"ebd0aeae-868c-487e-9e33-d91fc7f5d738"], Cell[1833969, 30161, 350, 10, 66, "Input",ExpressionUUID->"7b98161c-39b7-4c37-96f8-5e741d084b35"], Cell[CellGroupData[{ Cell[1834344, 30175, 371, 10, 59, "Input",ExpressionUUID->"e6db590d-e675-46ce-9849-a3d149f3dbf7"], Cell[1834718, 30187, 270, 6, 59, "Output",ExpressionUUID->"c082a2a7-06a9-49b2-b07d-4c50d03795a7"] }, Open ]], Cell[1835003, 30196, 157, 6, 87, "Text",ExpressionUUID->"41edb4b6-3097-48d3-a8aa-576d0b2b27f7"], Cell[1835163, 30204, 375, 7, 103, "Text",ExpressionUUID->"afa89ba1-140e-41d1-aa8b-4c4c34f340f7"], Cell[1835541, 30213, 71, 0, 51, "Text",ExpressionUUID->"a5f40b10-2398-44c7-89d6-5f53beda8f95"] }, Open ]] } ] *)