Logistic Growth
Author: Andreas Bauer

This applet depicts a logistic growth sequence. Experiment with the starting population size, the maximum population and the combined factor for birth and starvation to explore the sequence's forms.

1/k

Starting population

Maximum population:

Starting population:

Explicit equation:

x

f(x)

Combined factor for birth and starvation:

k = 800 (slider from 1 to 5000, step 1)
f_0 = 2 (slider from 0 to 150, step 1)
G = 122 (slider from 0 to 150, step 1)
f = Function(G / (1.0 + exp(-(G) * x / k) * (G / f_0 - 1.0)), 0.0, Infinity)
Liste1 = Sequence((n, f(n)), n, 0.0, 100.0)
A2 = 0
A3 = 1
A4: 2.0 * A3 - A2
A5: 2.0 * A4 - A3
A6: 2.0 * A5 - A4
A7: 2.0 * A6 - A5
A8: 2.0 * A7 - A6
A9: 2.0 * A8 - A7
A10: 2.0 * A9 - A8
A11: 2.0 * A10 - A9
A12: 2.0 * A11 - A10
A13: 2.0 * A12 - A11
A14: 2.0 * A13 - A12
A15: 2.0 * A14 - A13
A16: 2.0 * A15 - A14
A17: 2.0 * A16 - A15
A18: 2.0 * A17 - A16
A19: 2.0 * A18 - A17
A20: 2.0 * A19 - A18
A21: 2.0 * A20 - A19
A22: 2.0 * A21 - A20
A23: 2.0 * A22 - A21
A24: 2.0 * A23 - A22
A25: 2.0 * A24 - A23
A26: 2.0 * A25 - A24
A27: 2.0 * A26 - A25
A28: 2.0 * A27 - A26
A29: 2.0 * A28 - A27
A30: 2.0 * A29 - A28
A31: 2.0 * A30 - A29
A32: 2.0 * A31 - A30
A33: 2.0 * A32 - A31
A34: 2.0 * A33 - A32
A35: 2.0 * A34 - A33
A36: 2.0 * A35 - A34
A37: 2.0 * A36 - A35
A38: 2.0 * A37 - A36
A39: 2.0 * A38 - A37
A40: 2.0 * A39 - A38
A41: 2.0 * A40 - A39
A42: 2.0 * A41 - A40
A43: 2.0 * A42 - A41
A44: 2.0 * A43 - A42
A45: 2.0 * A44 - A43
A46: 2.0 * A45 - A44
A47: 2.0 * A46 - A45
A48: 2.0 * A47 - A46
A49: 2.0 * A48 - A47
A50: 2.0 * A49 - A48
A51: 2.0 * A50 - A49
A52: 2.0 * A51 - A50
A53: 2.0 * A52 - A51
A54: 2.0 * A53 - A52
A55: 2.0 * A54 - A53
A56: 2.0 * A55 - A54
A57: 2.0 * A56 - A55
A58: 2.0 * A57 - A56
A59: 2.0 * A58 - A57
A60: 2.0 * A59 - A58
A61: 2.0 * A60 - A59
A62: 2.0 * A61 - A60
A63: 2.0 * A62 - A61
A64: 2.0 * A63 - A62
A65: 2.0 * A64 - A63
A66: 2.0 * A65 - A64
A67: 2.0 * A66 - A65
A68: 2.0 * A67 - A66
A69: 2.0 * A68 - A67
A70: 2.0 * A69 - A68
A71: 2.0 * A70 - A69
A72: 2.0 * A71 - A70
A73: 2.0 * A72 - A71
A74: 2.0 * A73 - A72
A75: 2.0 * A74 - A73
A76: 2.0 * A75 - A74
A77: 2.0 * A76 - A75
A78: 2.0 * A77 - A76
A79: 2.0 * A78 - A77
A80: 2.0 * A79 - A78
A81: 2.0 * A80 - A79
A82: 2.0 * A81 - A80
A83: 2.0 * A82 - A81
A84: 2.0 * A83 - A82
A85: 2.0 * A84 - A83
A86: 2.0 * A85 - A84
A87: 2.0 * A86 - A85
A88: 2.0 * A87 - A86
A89: 2.0 * A88 - A87
A90: 2.0 * A89 - A88
A91: 2.0 * A90 - A89
A92: 2.0 * A91 - A90
A93: 2.0 * A92 - A91
A94: 2.0 * A93 - A92
A95: 2.0 * A94 - A93
A96: 2.0 * A95 - A94
A97: 2.0 * A96 - A95
A98: 2.0 * A97 - A96
A99: 2.0 * A98 - A97
A100: 2.0 * A99 - A98
A101: 2.0 * A100 - A99
A102: 2.0 * A101 - A100
B2: f(A2)
B3: f(A3)
B4: f(A4)
B5: f(A5)
B6: f(A6)
B7: f(A7)
B8: f(A8)
B9: f(A9)
B10: f(A10)
B11: f(A11)
B12: f(A12)
B13: f(A13)
B14: f(A14)
B15: f(A15)
B16: f(A16)
B17: f(A17)
B18: f(A18)
B19: f(A19)
B20: f(A20)
B21: f(A21)
B22: f(A22)
B23: f(A23)
B24: f(A24)
B25: f(A25)
B26: f(A26)
B27: f(A27)
B28: f(A28)
B29: f(A29)
B30: f(A30)
B31: f(A31)
B32: f(A32)
B33: f(A33)
B34: f(A34)
B35: f(A35)
B36: f(A36)
B37: f(A37)
B38: f(A38)
B39: f(A39)
B40: f(A40)
B41: f(A41)
B42: f(A42)
B43: f(A43)
B44: f(A44)
B45: f(A45)
B46: f(A46)
B47: f(A47)
B48: f(A48)
B49: f(A49)
B50: f(A50)
B51: f(A51)
B52: f(A52)
B53: f(A53)
B54: f(A54)
B55: f(A55)
B56: f(A56)
B57: f(A57)
B58: f(A58)
B59: f(A59)
B60: f(A60)
B61: f(A61)
B62: f(A62)
B63: f(A63)
B64: f(A64)
B65: f(A65)
B66: f(A66)
B67: f(A67)
B68: f(A68)
B69: f(A69)
B70: f(A70)
B71: f(A71)
B72: f(A72)
B73: f(A73)
B74: f(A74)
B75: f(A75)
B76: f(A76)
B77: f(A77)
B78: f(A78)
B79: f(A79)
B80: f(A80)
B81: f(A81)
B82: f(A82)
B83: f(A83)
B84: f(A84)
B85: f(A85)
B86: f(A86)
B87: f(A87)
B88: f(A88)
B89: f(A89)
B90: f(A90)
B91: f(A91)
B92: f(A92)
B93: f(A93)
B94: f(A94)
B95: f(A95)
B96: f(A96)
B97: f(A97)
B98: f(A98)
B99: f(A99)
B100: f(A100)
B101: f(A101)
B102: f(A102)
Text4: "k = \frac{1}{" + k + "}"
Text3: "f(x) = " + G + " \cdot \frac{1}{1 + e^{\frac{" + G + " \cdot x}{" + k + "}} \cdot \left( \frac{" + G + "}{" + f_0 + "} - 1\right)}"