{"text_format":"2","workbook":"xls","n_sheets":8,"sheets":["NumVsAnlytl","ModelFitHigh","ModelFitLow","ModelFitMed","UNEPGrowthrate","UNEPWP3","UNEPWP2","UNEPWP1"],"not_rendered":{"charts":6,"images":0,"macros":0,"external_links":1,"defined_names":1,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"run_cost":"one","rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900","formulas":"cached_only"}

{"sheet":"NumVsAnlytl","index":0,"n_rows":111,"n_cols":3,"rows_kept":111,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[null,"if the time step gets too large the numerical solution doesn't work"]
["time Step, DT",70]
[]
[null,"Analytical ","Numerical "]
[null,"Model","Model"]
["Initial Population",2.52]
["Carrying Capacity",500]
["initial growth rate",2.8]
[null,"Logistic"]
["Year","Population","Numerical"]
[1950,2.52,2.52]
[2020,17.35674723422403,7.434306432]
[2090,101.69041909788406,21.788892903190487]
[2160,322.22181424469613,62.63408004597275]
[2230,463.9444341497908,170.01860724191448]
[2300,494.58584302599223,389.94227634682375]
[2370,499.2302089901162,558.173620767031]
[2440,499.89142483948865,430.88737706331653]
[2510,499.9847034205654,547.6240237943985]
[2580,499.9978452913414,445.39019039928934]
[2650,499.99969649001713,540.7350705025488]
[2720,499.9999572480408,454.3896961196705]
[2790,499.99999397802605,535.6311164304968]
[2860,499.99999915175414,460.8173885110351]
[2930,499.9999998805174,531.5970210204732]
[3000,499.99999998316986,465.75324260986224]
[3070,499.9999999976293,528.2793527589156]
[3140,499.9999999996661,469.71691192498537]
[3210,499.999999999953,525.4768680924464]
[3280,499.99999999999335,472.99784906467596]
[3350,499.9999999999991,523.0639295697857]
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[3560,500.00000000000006,478.159885547819]
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[3910,500,515.95725943802]
[3980,500,483.6828651547135]
[4050,500.00000000000006,514.6207538044026]
[4120,500,485.12611189588233]
[4190,500,513.4117009944044]
[4260,500,486.4196620490035]
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[4960,500,491.2408472062251]
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[5170,500.00000000000006,507.46627300075113]
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[5940,500.00000000000006,495.14547357218777]
[6010,500,504.56796497749355]
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[6150,500,504.21013908866047]
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[6290,500,503.8805116852982]
[6360,500,496.21567996802986]
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[6500,500,496.51611298526853]
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[6640,500,496.7923154540168]
[6710,500,503.0390433427695]
[6780,500,497.0463141159395]
[6850,500,502.8013393483155]
[6920,500,497.279952017211]
[6990,500,502.58224331224505]
[7060,499.99999999999994,497.494907936592]
[7130,500,502.38028847478677]
[7200,499.99999999999994,497.69271323316974]
[7270,500,502.1941268930375]
[7340,500.00000000000006,497.87476654681893]
[7410,500,502.02251897551014]
[7480,500,498.0423466981257]
[7550,500,501.864324136514]
[7620,500,498.1966240673614]
[7690,500,501.7184924094957]
[7760,500.00000000000006,498.338670679531]
[7830,500,501.584056888415]
[7900,500,498.46946918111666]
[7970,500,501.4601268897448]
[8040,500,498.589920861351]
[8110,500,501.3458817462482]
[8180,500,498.7008528447163]
[8250,500,501.24056515841454]
[8320,500,498.80302456042597]
[8390,500,501.1434800411955]
[8460,500,498.8971335777623]
[8530,500,501.05398381311454]
[8600,500,498.98382088244716]
[8670,500,500.9714840824549]
[8740,500,499.0636756580593]
[8810,500,500.89543469143166]
[8880,500,499.1372396273422]
[8950,500,500.8253320843458]

{"sheet":"ModelFitHigh","index":1,"n_rows":31,"n_cols":6,"rows_kept":31,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[]
[]
[]
[]
[]
[null,"Initial Population",null,"Po(billions)=","Po(billions)=",2.52]
[null,"Carrying Capacity",null,"Pmax(billions)=","Pmax(billions)=",15]
[null,"initial growth rate",null,"r(%/yr)=","r(%/yr)=",2.5]
[null,"data from    http://esa.un.org/unpp/"]
[null,"Year","Low","Mediem","High","Population"]
[null,1950,2.518629,2.518629,2.518629,2.52]
[null,1955,2.755823,2.755823,2.755823,2.7930563905888683]
[null,1960,3.021475,3.021475,3.021475,3.088378163720006]
[null,1965,3.334874,3.334874,3.334874,3.406212401776571]
[null,1970,3.692492,3.692492,3.692492,3.746468123767178]
[null,1975,4.068109,4.068109,4.068109,4.108667682902324]
[null,1980,4.434682,4.434682,4.434682,4.491906772101809]
[null,1985,4.830979,4.830979,4.830979,4.894827251788717]
[null,1990,5.263593,5.263593,5.263593,5.315606824580103]
[null,1995,5.67438,5.67438,5.67438,5.751968899314087]
[null,2000,6.070581,6.070581,6.070581,6.201214788143237]
[null,2005,6.403651,6.453628,6.501617,6.660278724456626]
[null,2010,6.688557,6.830283,6.966491,7.125804227992766]
[null,2015,6.939483,7.197247,7.446772,7.594238309703834]
[null,2020,7.159031,7.540237,7.912776,8.061938183153122]
[null,2025,7.334237,7.851455,8.364838,8.525283807923614]
[null,2030,7.454422,8.130149,8.81759,8.980788948899637]
[null,2035,7.518174,8.378184,9.278887,9.425203599506842]
[null,2040,7.529259,8.593591,9.740745,9.855601559701865]
[null,2045,7.492193,8.774394,10.193284,10.26944852617626]
[null,2050,7.408573,8.918724,10.633442,10.664647996409435]

{"sheet":"ModelFitLow","index":2,"n_rows":31,"n_cols":6,"rows_kept":31,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[]
[]
[]
[]
[]
[null,null,"Initial Population",null,"Po(billions)=",2.52]
[null,null,"Carrying Capacity",null,"Pmax(billions)=",9]
[null,null,"initial growth rate",null,"r(%/yr)=",3]
[null,"data from    http://esa.un.org/unpp/"]
[null,"Year","Low","Mediem","High","Population"]
[null,1950,2.518629,2.518629,2.518629,2.52]
[null,1955,2.755823,2.755823,2.755823,2.8009033130222085]
[null,1960,3.021475,3.021475,3.021475,3.098148157472713]
[null,1965,3.334874,3.334874,3.334874,3.4095878216097146]
[null,1970,3.692492,3.692492,3.692492,3.7325349690550396]
[null,1975,4.068109,4.068109,4.068109,4.063834991133805]
[null,1980,4.434682,4.434682,4.434682,4.399977856835183]
[null,1985,4.830979,4.830979,4.830979,4.737241214629555]
[null,1990,5.263593,5.263593,5.263593,5.071852934721897]
[null,1995,5.67438,5.67438,5.67438,5.400158290230055]
[null,2000,6.070581,6.070581,6.070581,5.718776246434419]
[null,2005,6.403651,6.453628,6.501617,6.024731030194112]
[null,2010,6.688557,6.830283,6.966491,6.315548888950481]
[null,2015,6.939483,7.197247,7.446772,6.58931488157123]
[null,2020,7.159031,7.540237,7.912776,6.844689650358016]
[null,2025,7.334237,7.851455,8.364838,7.080890486250205]
[null,2030,7.454422,8.130149,8.81759,7.297644012131962]
[null,2035,7.518174,8.378184,9.278887,7.495119260408501]
[null,2040,7.529259,8.593591,9.740745,7.673849947515405]
[null,2045,7.492193,8.774394,10.193284,7.83465371166633]
[null,2050,7.408573,8.918724,10.633442,7.978554425200658]

{"sheet":"ModelFitMed","index":3,"n_rows":34,"n_cols":5,"rows_kept":34,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[]
[]
[]
[]
["Name:","Jane Smyth"]
["Date:","5007-03-04"]
["Assignment:","XL World Population",null,null,"Logistic Growth"]
[{"$nulls":4},"Model"]
["Initial Population",null,null,"Po(billions)=",2.52]
["Carrying Capacity",null,null,"Pmax(billions)=",10.8]
["initial growth rate",null,null,"r(%/yr)=",2.8]
["data from    http://esa.un.org/unpp/"]
["Year","Low","Mediem","High","Population"]
[1950,2.518629,2.518629,2.518629,0]
[1955,2.755823,2.755823,2.755823,2.8004937774439562]
[1960,3.021475,3.021475,3.021475,3.100517541759546]
[1965,3.334874,3.334874,3.334874,3.4189461484416688]
[1970,3.692492,3.692492,3.692492,3.754132437905038]
[1975,4.068109,4.068109,4.068109,4.103908802272052]
[1980,4.434682,4.434682,4.434682,4.465619504079165]
[1985,4.830979,4.830979,4.830979,4.836185329335963]
[1990,5.263593,5.263593,5.263593,5.212198790212344]
[1995,5.67438,5.67438,5.67438,5.590044499484503]
[2000,6.070581,6.070581,6.070581,5.966036127810052]
[2005,6.403651,6.453628,6.501617,6.336559130203575]
[2010,6.688557,6.830283,6.966491,6.698207635153536]
[2015,6.939483,7.197247,7.446772,7.047904692062499]
[2020,7.159031,7.540237,7.912776,7.382997304797602]
[2025,7.334237,7.851455,8.364838,7.701320894334748]
[2030,7.454422,8.130149,8.81759,8.001231427005717]
[2035,7.518174,8.378184,9.278887,8.281606809066774]
[2040,7.529259,8.593591,9.740745,8.541821808145304]
[2045,7.492193,8.774394,10.193284,8.781702453929903]
[2050,7.408573,8.918724,10.633442,9.001466552814865]

{"sheet":"UNEPGrowthrate","index":4,"n_rows":34,"n_cols":9,"rows_kept":34,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[]
[]
["Name:","Jane Smyth"]
["Date:","5007-03-04"]
["Assignment:","XL World Population"]
[]
["UNEP World Population in thousands"]
["from    http://esa.un.org/unpp/"]
[]
[]
[null,"UNEP Projections"]
[]
["Year","Low","Mediem","High"]
[1950,2.518629,2.518629,2.518629]
[1955,2.755823,2.755823,2.755823,null,1952.5,1.7988143602406477,1.7988143602406477,1.7988143602406477]
[1960,3.021475,3.021475,3.021475,null,1957.5,1.839281961913685,1.839281961913685,1.839281961913685]
[1965,3.334874,3.334874,3.334874,null,1962.5,1.972195044671084,1.972195044671084,1.972195044671084]
[1970,3.692492,3.692492,3.692492,null,1967.5,2.0355734993737338,2.0355734993737338,2.0355734993737338]
[1975,4.068109,4.068109,4.068109,null,1972.5,1.9360201613251329,1.9360201613251329,1.9360201613251329]
[1980,4.434682,4.434682,4.434682,null,1977.5,1.7244831726429588,1.7244831726429588,1.7244831726429588]
[1985,4.830979,4.830979,4.830979,null,1982.5,1.7108201994439494,1.7108201994439494,1.7108201994439494]
[1990,5.263593,5.263593,5.263593,null,1987.5,1.714244051159376,1.714244051159376,1.714244051159376]
[1995,5.67438,5.67438,5.67438,null,1992.5,1.5022417773384522,1.5022417773384522,1.5022417773384522]
[2000,6.070581,6.070581,6.070581,null,1997.5,1.3493480310407147,1.3493480310407147,1.3493480310407147]
[2005,6.403651,6.453628,6.501617,null,2002.5,1.0680256708388947,1.223381053446171,1.3713942462567028]
[2010,6.688557,6.830283,6.966491,null,2007.5,0.87045974216114,1.1341689958627381,1.3806660891047202]
[2015,6.939483,7.197247,7.446772,null,2012.5,0.7364991590867058,1.0464108791783024,1.3328862451202055]
[2020,7.159031,7.540237,7.912776,null,2017.5,0.6228968528172533,0.930932308391311,1.213587795682529]
[2025,7.334237,7.851455,8.364838,null,2022.5,0.48355139779379,0.8087947705814262,1.110880255546054]
[2030,7.454422,8.130149,8.81759,null,2027.5,0.32507342281676854,0.6975369931578828,1.053988411882182]
[2035,7.518174,8.378184,9.278887,null,2032.5,0.17031649020650802,0.600993449792901,1.0196393474818333]
[2040,7.529259,8.593591,9.740745,null,2037.5,0.029466820021726143,0.5076829029373788,0.9713289931161679]
[2045,7.492193,8.774394,10.193284,null,2042.5,-0.0987015103466679,0.41640524217403274,0.9080733252670592]
[2050,7.408573,8.918724,10.633442,null,2047.5,-0.22447168152295174,0.32629635997453943,0.8453714712528513]

{"sheet":"UNEPWP3","index":5,"n_rows":34,"n_cols":4,"rows_kept":34,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[]
[]
["Name:","Jane Smyth"]
["Date:","5007-03-04"]
["Assignment:","XL World Population"]
[]
["UNEP World Population in thousands"]
["from    http://esa.un.org/unpp/"]
[]
[]
[null,"UNEP Projections"]
[]
["Year","Low","Mediem","High"]
[1950,2.518629,2.518629,2.518629]
[1955,2.755823,2.755823,2.755823]
[1960,3.021475,3.021475,3.021475]
[1965,3.334874,3.334874,3.334874]
[1970,3.692492,3.692492,3.692492]
[1975,4.068109,4.068109,4.068109]
[1980,4.434682,4.434682,4.434682]
[1985,4.830979,4.830979,4.830979]
[1990,5.263593,5.263593,5.263593]
[1995,5.67438,5.67438,5.67438]
[2000,6.070581,6.070581,6.070581]
[2005,6.403651,6.453628,6.501617]
[2010,6.688557,6.830283,6.966491]
[2015,6.939483,7.197247,7.446772]
[2020,7.159031,7.540237,7.912776]
[2025,7.334237,7.851455,8.364838]
[2030,7.454422,8.130149,8.81759]
[2035,7.518174,8.378184,9.278887]
[2040,7.529259,8.593591,9.740745]
[2045,7.492193,8.774394,10.193284]
[2050,7.408573,8.918724,10.633442]

{"sheet":"UNEPWP2","index":6,"n_rows":34,"n_cols":5,"rows_kept":34,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[]
[]
["Name:","Jane Smyth"]
["Date:","5007-03-04"]
["Assignment:","XL World Population"]
[]
[]
[]
[]
[]
[null,"UNEP World Population in thousands"]
[null,"from    http://esa.un.org/unpp/"]
[null,"Year","Low","Mediem","High"]
[null,1950,2.518629,2.518629,2.518629]
[null,1955,2.755823,2.755823,2.755823]
[null,1960,3.021475,3.021475,3.021475]
[null,1965,3.334874,3.334874,3.334874]
[null,1970,3.692492,3.692492,3.692492]
[null,1975,4.068109,4.068109,4.068109]
[null,1980,4.434682,4.434682,4.434682]
[null,1985,4.830979,4.830979,4.830979]
[null,1990,5.263593,5.263593,5.263593]
[null,1995,5.67438,5.67438,5.67438]
[null,2000,6.070581,6.070581,6.070581]
[null,2005,6.403651,6.453628,6.501617]
[null,2010,6.688557,6.830283,6.966491]
[null,2015,6.939483,7.197247,7.446772]
[null,2020,7.159031,7.540237,7.912776]
[null,2025,7.334237,7.851455,8.364838]
[null,2030,7.454422,8.130149,8.81759]
[null,2035,7.518174,8.378184,9.278887]
[null,2040,7.529259,8.593591,9.740745]
[null,2045,7.492193,8.774394,10.193284]
[null,2050,7.408573,8.918724,10.633442]

{"sheet":"UNEPWP1","index":7,"n_rows":24,"n_cols":4,"rows_kept":24,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["UNEP World Population in thousands"]
["from    http://esa.un.org/unpp/"]
["Year","Low","Mediem","High"]
[1950,2.518629,2.518629,2.518629]
[1955,2.755823,2.755823,2.755823]
[1960,3.021475,3.021475,3.021475]
[1965,3.334874,3.334874,3.334874]
[1970,3.692492,3.692492,3.692492]
[1975,4.068109,4.068109,4.068109]
[1980,4.434682,4.434682,4.434682]
[1985,4.830979,4.830979,4.830979]
[1990,5.263593,5.263593,5.263593]
[1995,5.67438,5.67438,5.67438]
[2000,6.070581,6.070581,6.070581]
[2005,6.403651,6.453628,6.501617]
[2010,6.688557,6.830283,6.966491]
[2015,6.939483,7.197247,7.446772]
[2020,7.159031,7.540237,7.912776]
[2025,7.334237,7.851455,8.364838]
[2030,7.454422,8.130149,8.81759]
[2035,7.518174,8.378184,9.278887]
[2040,7.529259,8.593591,9.740745]
[2045,7.492193,8.774394,10.193284]
[2050,7.408573,8.918724,10.633442]