Change the assumptions.
For continuous growth, doubling time = 69.3147 ÷ the percentage rate. That connection gives 69 a useful mathematical role—without making claims about how quickly people learn.
Linear growth adds the same amount each year. Annual growth compounds once per year. Continuous growth uses eʳᵗ. Constant rates are simplifying assumptions; this is a mathematical simulation.
See the difference
LinearAnnualContinuous
Continuous doubling time6.93 yr
Annual doubling time7.27 yr
| Year | Linear | Annual | Continuous |
|---|---|---|---|
| 0 | 100 | 100 | 100 |
| 1 | 110 | 110 | 110.52 |
| 2 | 120 | 121 | 122.14 |
| 3 | 130 | 133.1 | 134.99 |
| 4 | 140 | 146.41 | 149.18 |
| 5 | 150 | 161.05 | 164.87 |
| 6 | 160 | 177.16 | 182.21 |
| 7 | 170 | 194.87 | 201.38 |
| 8 | 180 | 214.36 | 222.55 |
| 9 | 190 | 235.79 | 245.96 |
| 10 | 200 | 259.37 | 271.83 |
| 11 | 210 | 285.31 | 300.42 |
| 12 | 220 | 313.84 | 332.01 |
Keep this useful.
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