Verified calculation capability

Exponential growth / decay Calculation Capability

Periodic x₀(1+r/100)^t or continuous x₀e^(kt) growth and decay. Any three of x₀, r/k, t, x(t) solve the fourth; all four verify displayed-precision consistency. · Math

Capability ID math.exponential_growth · version 1.0.7

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Periodic

Periodic: x(t) = x₀ × (1 + r/100)^t
Continuous: x(t) = x₀ × e^(k t)
Doubling time: t₂ = ln(2) / ln(1 + r/100) (r > 0)
Half-life: t½ = ln(1/2) / ln(1 + r/100) (−100 < r < 0)

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`formula`	—	—	output
`api_version`	—	—	output
`api_contract_version`	—	—	output
`spec_version`	—	—	output
`page`	Canonical calculator page URL	—	output
`links`	—	—	output
`consistency`	Present when x₀, r/k, t, and x(t) are all supplied (verify mode). Display-quantization comparison of calculated vs provided x(t).	—	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

Assumptions

Constant rate over the interval (real populations often need logistic models long-term).
CalculatorX defines the periodic model domain as r > −100% so the growth factor stays positive and inverse/logarithmic solving remains well-defined.

Example

One numerical check. The calculator page holds worked steps and FAQ.

50 × (1.04)^90 ≈ 1705.97

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 7/7 declared partitions (forward-periodic, forward-continuous, inverse-time, inverse-x0, inverse-rate, verify, invalid-domain)
Calculation version: 1.0.7
Verification: 20/20 calculation tests · 14/14 legacy golden · 6/6 legacy boundary
Production surface contract: 27/27
Versions: Calculation 1.0.7 · CVP protocol 1.0.0-proposed
CVP identity: 3/3 property · digest 4da3d88a831d
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP / URL→result→graph
Success 1/1. Integration: URL → SSR result → Live graph current point (4/4). Hydration/slider/history are URL-canonical contracts, not a live browser session.
CVP suite: 5/5 golden · 6/6 CVP boundary · 6/6 invalid · 3/3 property · 1/1 metamorphic · 3/3 round-trip · 13/13 O3 · 1/1 cross-interface · 4/4 URL→result→graph · 24/24 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.7 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.7 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 27/27.

Tool id: exponential-growth
Engine: exponential-growth
REST: POST /api/v1/calc/exponential-growth
MCP: execute_calculation with capability_id: "math.exponential_growth"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.7)
Versioned output schema: Immutable pin (1.0.7)

Operations

Declared calculation modes for this capability.

solve-xt
solve-t
solve-x0
solve-rate
verify

References

Human-readable sources plus CVP reference evidence classes.

Sources

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"math.exponential_growth"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.7) when reproducibility matters. Full protocol notes: MCP docs.