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[null,null,"   The Logistic Growth Model",{"$nulls":19},{"$f":"#REF!","v":{"$error":"#REF!"}},{"$f":"#REF!","v":{"$error":"#REF!"}},0,{"$f":"a","v":0.29000000000000004}]
[{"$nulls":22},{"$f":"E15","v":3.3799999999999998E-3},{"$f":"#REF!","v":{"$error":"#REF!"}},{"$f":"x.one","v":{"$error":"#NAME?"}},{"$f":"a*U1^Y2","v":{"$error":"#NAME?"}}]
[null,null,"This program lets you investigate the",{"$nulls":19},{"$f":"E18","v":18},{"$f":"#REF!","v":{"$error":"#REF!"}}]
[null,null,"            behavior of the solution",{"$nulls":21},0,{"$f":"a","v":0.29000000000000004}]
[null,null,"of the continuous logistic growth model "]
[]
[]
[null,null,"         based on values for a and b."]
[]
[]
[]
[null,"Enter the initial growth rate a",null,null,{"$f":"F12/100+0.01","v":{"v":0.29000000000000004,"d":"0.29"}},28]
[null,null,"a is between 0.01 (1%) and 0.50 (50%)"]
[]
[null,"Enter the inhibiting constant b",null,null,{"$f":"F15/50000+0.0001","v":{"v":3.3799999999999998E-3,"d":"0.0034"}},164]
[null,null,"b is between 0.0001 and 0.005"]
[]
[null,"What is the initial population P0?",null,null,{"$f":"F18+1","v":18},17]
[null,null,"P0 is between 1 and 1000",{"$nulls":6},"The limiting (or maximum sustainable) population is"]
[{"$nulls":10},"L = a/b =",{"$f":"a/b","v":{"v":85.79881656804736,"d":"86"}}]
[]
[{"$nulls":9},"Trace along the population curve:"]
["Click each item below for suggestions and investigations",{"$nulls":8},"t =",{"$f":"L23/2","v":25.5},51]
[{"$nulls":3},"   Item 1",{"$nulls":5},"P =",{"$f":"LOOKUP(t0+0.001,Sheet3!A1:A203,Sheet3!B1:B203)","v":{"v":85.56992186119656,"d":"86"}}]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    ",{"$nulls":7}," "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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[null,null,"   The Logistic Growth Model",{"$nulls":18},-2,{"$f":"a*V1^2+b*V1+cc","v":1.15324},0,1]
[{"$nulls":21},1,{"$f":"a*V2^2+b*V2+cc","v":{"v":0.29338000000000003,"d":"0.29338"}}]
[null,null,"This program lets you investigate the",{"$nulls":18},3,{"$f":"a*V3^2+b*V3+cc","v":2.62014}]
[null,null,"            behavior of the solution"]
[null,null,"of the continuous logistic growth model ",{"$nulls":17},{"$f":"a","v":0.29000000000000004},{"$f":"-b/2/a","v":-0.00582758620689655},{"$f":"a*V5^2+b*V5+cc","v":{"v":-9.84862068965517e-06,"d":"-0.00001"}}]
[{"$nulls":20},{"$f":"b","v":3.3799999999999998E-3}]
[{"$nulls":20},{"$f":"cc","v":0}]
[null,null,"      based on values for a and L."]
[]
[]
[null,"Enter the initial growth rate a",null,null,{"$f":"F11/100+0.01","v":{"v":0.09999999999999999,"d":"0.10"}},9]
[null,null,"a is between 0.01 (1%) and 0.50 (50%)"]
[]
[null,"Enter a value for the maximum sustainable population"]
[null,null,"L is between 1 and 5000",null,{"$f":"F15+1","v":2478},2477]
[]
[]
[null,"What is the initial population P0?",null,null,{"$f":"F18+1","v":213},212,{"$nulls":3},"The inhibiting constant is"]
[null,null,"P0 is between 1 and 1000",{"$nulls":7},"b = a/L =",{"$f":"aa/LL","v":{"v":4.0355125100887808E-5,"d":"0.00004"}}]
[]
[{"$nulls":9},"Trace along the population curve:"]
[{"$nulls":9},"t =",{"$f":"L22/2","v":68},136]
["Click each item below for suggestions and investigations",{"$nulls":8},"P =",{"$f":"LOOKUP(t00+0.001,Sheet3!F1:F201,Sheet3!G1:G201)","v":{"v":2448.994923790096,"d":"2449"}}]
[{"$nulls":3},"   Item 1"]
[{"$nulls":3},"   Item 2"]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4"]
[]
[]
[]
["To access/download all the DIGMath Apps for Calculus"]
["Click this link:",null,null,"DIGMath for Calculus"]
[]
["Created by:  Sheldon P. Gordon   "]
["                      Farmingdale State College    "]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]
{"$rows_empty":817}
[{"$nulls":20},{"$f":"X856","v":0},{"$f":"X856","v":0}]

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