LMv/3$ ArialY38Z3$ArialY38Z3$ ArialY38Z3@TMonth' 'D', 'YYYY Normal Comma Currency Percent Fixed DateHeading 1Heading 2 Total Comma0 Currency0033@R033@2033@B033@033@x033@033@033@0 33@P033@0033@033@033@QSTAT BETAINV alpha beta dBY!_]<  ?xNQ$$  A   ?     d~@$.  $ 4!p(\Y @ @ @ P@  B>?@p07 $. H\ 64!p(\ B@̀ d,$. $H`H7N ~M Z | Bx_~??@___ ? ڂ*'""" "    $ $       Mq  d2X, X1Axis? Ms  d2X, Y1Axis?  Mt  d2X, Y2Axis? vj  d2X, 1PaneLeftWallRightWallBaseSeriesSeriesLabel?  Rm  d2X,  X1Title? Ro  d2X,  Y1Title? Rp  d2X,  Y2Title? Ml  d2X, Legend? }Z   Title? $ArialArial "]ZY Beta-dist. R!_]<  ?l`NQ$$  A   ?      $P$. @H 4!p(\Y ?@ @ @ @  B0=@! ?@p073h0Ά $. n Ci9Fi7H\ 6/ b*MQ)4!p(\@ Ph!8Pt B0:`0@̀B3@ : P d's0$. @?};?O~}7<AxO~@$H`H7N ~M Z |@ Bx_~??@___ ? ڂ*'""" "  t      u  u  u )$ $       Mq  q X1Axis? Ms  H& Y1Axis?  Mt  d2X, Y2Axis? vj  Ht 1PaneLeftWallRightWallBaseSeriesSeriesLabel?  Rm  ^q^  X1Title? Ro  Z-  Y1Title? Rp  d2X,  Y2Title? Ml  Of Legend? }Z   Title? Stochastic R Beta distribution$ArialArial "]PZYDeterministic R!_]<  ?l``;Q$$  A   ?      P$.  H 4!p(\Y ?@ @ @ @  B0 ?@p07C)i:Eqp2Sq@P7 o7#yh$. Oyn:L&@p: 'CI #sH\ 6/̀b*MQ)4!p(\@ Ph_@!8Pt B0b: 0@̀B2@p:`P dr($. @?};?O~}7<AxO~@$H`H7N ~M Z |@ Bx_~??@___ ? ڂ*'""" "  t      t  t  t $ $       Mq  l X1Axis? Ms  CH  Y1Axis?  Mt  d2X, Y2Axis? vj  Ht 1PaneLeftWallRightWallBaseSeriesSeriesLabel?  Rm  ^l^  X1Title? -Ro  Z_  Y1Title? -Rp  d2X,  Y2Title? .Ml  E Legend? }Z  ,T Title? CDensity-independent Population Growth Exponential Population GrowthArial&Arial "]Z  %&'( @@0d  $ ArialOYZ$ ArialOYZ  LB  %&'( @@0d  $ ArialOYZ$ ArialOYZ  B           ^  ddư>   ?&  Mb@?   #       f  g    i2      -./g  0d    s\TEMP\QPW4280.TMP6$u<7~\o76t t t tvv v v v t-'Density-independent population growth%Exponential Population GrowthwiThe first 4 columns provide a model demonstrating exponential growth. You can change the values of N0 or R to pichange the graph. Columns F-I demonstrate exponential growth where the parameter R is a random variablewithat changes each year. R is modeled as a beta variable with parameters alpha and beta (which can be changed).qiThe mean is alpha/(alpha + beta), and the variance is (alpha beta)/((alpha + beta)^2 (alpha + beta + 1)).wiHit the F9 key to recalculate the spreadsheet, i.e., generate a new set of R's and hence a different populationiprojection.  h  h  h "N0 "R "Time  ?   @   @   @   @   @   @    @   "@   $@   &@   (@   *@   ,@   .@   0@   !1@   "2@   #3@   $4@   %5@   &6@   '7@   (8@   )9@   *:@   +;@   ,<@   -=@   .>@   /?@   0@@   1@@   2A@   3A@   4B@   5B@   6C@   7C@   8D@   9D@   :E@   ;E@   <F@   =F@   >G@   ?G@   @H@   AH@   BI@   CI@   DJ@   EJ@   FK@   GK@   HL@   IL@   JM@   KM@   LN@   MN@   NO@   OO@   PP@   Q@P@   RP@   SP@   TQ@   U@Q@   VQ@   WQ@   XR@   Y@R@   ZR@   [R@   \S@   ]@S@   ^S@   _S@   `T@   a@T@   bT@   cT@   dU@   e@U@   fU@   gU@   hV@   i@V@   jV@   kV@   lW@   m@W@   nW@   oW@   pX@   q@X@   rX@   sX@   tY@     {Gz? 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"N(t)e@ ){Gz@    )8EGr@    )LN{@    )C@    )b@    )Z䴔@    )]G7@    )qD@    )Y@    )wv@    )nLj%@    )Υ@    )5@    )#KH3@    )Պ=o@    ) 3¹ @    )!% [r @    )"ys*= @    )#\\ @    )$<~ @    )%= @    )&L \@    )'%sϓ@    )(u)C@    ))@    )*'@@    )++3@    ),=wM@    )-/?@    ).$k@    )/[*@    )0Ię@    )1 7@    )2_)@    )3vQʂ@    )4K/@    )5C@    )6Br(@    )7T>V@    )8E@    )9V @    ):# T@    );'U^!@    )<D^"_@    )=5R@@    )>$ )@    )?5. @    )@a m @    )ABc^!@    )BV̨!@    )C a"@    )D Ձ"@    )E$a)#@    )FcD9#@    )GGT$@    )H9g>$@    )Ib(H %@    )J\a6&@    )K]RxH&@    )Lsg'@    )M1E(@    )NEOi)@    )Osxl)@    )PI2*@    )Q(uQ+@    )RHo)#,@    )S,@    )Thm-@    )Ucܲ.@    )Vu٫/@    )W/QrO0@    )X+0@    )Yx@jFM1@    )Zd1@    )[\%%[2@    )\7C&2@    )]ry3@    )^0#d4@    )_es4@    )`]"H5@    )a}5@    )b+ m6@    )cDSA7@    )dx7@    )eAw8@    )fP[i9@    )gH>!,:@    )h::@    )i;@    )j_w2֙<@    )k~u=@    )l@9W>@    )mNQv@?@    )n4e@@    )o E!X@@    )pEcUTA@    )qh%xA@    )rB@    )sY6qB@    )t3C7C@    vh  "Alpha  "Beta "Mean R  "SD R vh ? #@- {Gz?  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