logistic equation

2378 days ago by chrisphan

var('y') p = plot_slope_field(0.2*y*(1-y/100),(x,0,20),(y,-200,200)) p = p + plot(100/(1-exp(-0.2*x)/2), x, 0, 35, thickness=3, rgbcolor=(.75, 0, 0)) p = p + plot(100/(1-exp(-0.2*x)/3), x, 0, 25, thickness=3, rgbcolor=(0, .75, 0)) p = p + plot(100/(1-exp(-0.2*x)/-1), x, 0, 25, thickness=3, rgbcolor=(0, 0, .75)) p = p + plot(100/(1-exp(-0.2*x)/(-3/7)), x, 0, 25, thickness=3, rgbcolor=(.5, .5, 0)) p = p + plot(100, x, 0, 25, thickness=3, rgbcolor=(.5, 0, .5)) p = p + plot(0, x, 0, 25, thickness=3, rgbcolor=(.75, .5, 0)) p = p + plot(100/(1-exp(-0.2*x)/(1/6)), x, 0, log(6)/0.2, thickness=3, rgbcolor=(0, .5, 1)) show(p, ymin=-200, ymax=200, xmin=0, xmax=20, figsize=[9, 5]) 
       

                                
                            

                                
var('y') k = (-1/3)*log(17/26) p = plot_slope_field(k*y*(1-y/1500),(x,0,50),(y,0,1600)) p = p + plot(1500, x, 0, 55, rgbcolor=(1, 0, 0), thickness=3) p = p + plot(1500/(1 + 2*exp(-k*x)), x, 0, 55, thickness=3) show(p, ymin=0, ymax=1600, xmin=0, xmax= 50, figsize=[9,5]) 
       

                                
                            

                                
n(log(6)/0.2) 
       
8.95879734614027
8.95879734614027