This is a simple logistic growth and  model, built to reproduce the one that we made in InsightMaker.

Andy Long
Spring, 2018

Clear["Global`*"]

Manipulate[
lv=
NDSolve[
{(*  population: *)
pop'[t]==BirthRate  pop[t](1-pop[t]/K),
pop[0]==popinitial
},
{pop[t]},
{t,0,tend}];
p1=Plot[Evaluate[{pop[t]}/.lv],{t,0,tend},
PlotRange->All,AxesOrigin->{0,0}];
p2=Plot[K,{t,0,tend},PlotStyle->Dashed];
Show[p1,p2],
{{lv,{}},None},
{{tend,15},2,200,1},
{{popinitial,300},1,1000,1},
{{BirthRate,0.3},0,.6,.01},
{{K,200},10,600,10}
]