Source: https://guthlabs.ai/docs/instruments/population-growth-exponential-model/implementation/

instrument implementation / implementation-contract

# Population Growth: Exponential Model implementation

A source-bound implementation contract for Population Growth: Exponential Model; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t6-029

**Effect**: Computation or source lookup only

## Input and validation requirements

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.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "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."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/population-growth-exponential-model/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/population-growth-exponential-model/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/population-growth-exponential-model/qualification/>)

## 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`