Population Growth: Exponential Model mechanism

Model scope

The model is mathematically standard for idealized unconstrained growth and the stated educational, not-medical-advice label is appropriate. NEEDS_REVIEW is required because the exact units of r and time, the plotted time domain, and the behavior and labeling of doubling time for r<=0 are unspecified.

• N(t)=N0·e^(rt) is the standard unconstrained continuous exponential-growth model.
• The specification does not state the doubling-time formula. For r>0 it should be Td=ln(2)/r; for r=0 it is infinite/undefined, and for r<0 the population has a halving time ln(2)/|r| rather than a positive doubling time.
• The valid input domain and interpretation are not stated: normally N0>=0, t>=0 for forward prediction, and r may be positive, zero, or negative.

Units and conventions

• r must have inverse-time units and t must use the matching time unit, so rt is dimensionless.
• N0 and N(t) are population counts or consistently scaled population measures; they have the same units.
• Doubling-time output has the same time unit as t.
• The unit of r and time is ambiguous in the specification; this must be explicit in the interface and plot labels.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "N0": 1000,
    "r": 0.02,
    "r_unit": "per year",
    "sample_times": [
      0,
      10,
      20
    ],
    "time_unit": "years"
  },
  "expected_outputs": {
    "sampled_population": {
      "t=0": 1000,
      "t=10": 1221.402758,
      "t=20": 1491.824698
    },
    "doubling_time_years": 34.65735903,
    "curve_features": {
      "roots": [],
      "finite_extrema": [],
      "horizontal_asymptote": "N=0 as t approaches negative infinity",
      "initial_value": "N(0)=1000"
    }
  },
  "working": "N(0)=1000·e^(0.02·0)=1000·e^0=1000. N(10)=1000·e^(0.2)=1000·1.221402758=1221.402758. N(20)=1000·e^(0.4)=1000·1.491824698=1491.824698. Doubling time=ln(2)/0.02=0.6931471806/0.02=34.65735903 years. Since N0>0 and r>0, there are no roots or finite extrema; the horizontal asymptote is N=0 for t approaching negative infinity."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

The zero-growth input r=0 makes the requested doubling-time output undefined, so the instrument must reject it or explicitly display infinity/undefined. The specification also leaves unit conventions unenforced, allowing materially different population estimates from the same numeric inputs.

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json