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Exponential Population Growth (N_t = N₀·e^(rt))

Compute N_t = N₀·e^(rt) with fold change, doublings, doubling time, or half-life.

json· JSON resultOpen tool

Quick start

Call this tool from your code in three languages.

cURL

curl -X POST 'https://api.elysiatools.com/en/api/tools/exponential-growth-population' \
  -H 'Content-Type: application/json' \
  -d '{"n0":1000,"r":0.4,"t":10,"decimalPlaces":2}'

API reference

Send a POST request with your inputs as JSON. File parameters require a separate upload first.

Endpoint

HTTP

POST https://api.elysiatools.com/en/api/tools/exponential-growth-population

Parameters

Name	Type	Required	Description
n0	number	Yes	Population size at t = 0 (cells, individuals, biomass — any unit).
r	number	Yes	Constant per-capita rate: r > 0 growth, r < 0 decline, r = 0 stationary.
t	number	Yes	Time elapsed in the same unit as r.
decimalPlaces	number	No	—

Response format

JSON result

JSON

{
  "key": {...},
  "metadata": {
    "key": "value"
  },
  "error": "Error message (optional)",
  "message": "Notification message (optional)"
}

MCP integration

Add this tool to your Model Context Protocol server so AI agents can list and call it.

Server configuration

Add this block to your MCP client configuration:

mcp.json

{
  "mcpServers": {
    "elysiatools-exponential-growth-population": {
      "name": "exponential-growth-population",
      "description": "Compute N_t = N₀·e^(rt) with fold change, doublings, doubling time, or half-life.",
      "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=exponential-growth-population",
      "command": "",
      "args": [],
      "env": {},
      "isActive": true,
      "type": "sse"
    }
  }
}

List available tools

After connecting to the SSE endpoint, list the exposed tools:

tools/list

{
  "jsonrpc": "2.0",
  "id": 1,
  "method": "tools/list"
}

Call this tool

Invoke the tool by its id, passing arguments built from its parameters:

tools/call

{
  "jsonrpc": "2.0",
  "id": 2,
  "method": "tools/call",
  "params": {
    "name": "exponential-growth-population",
    "arguments": {
  "n0": 1000,
  "r": 0.4,
  "t": 10,
  "decimalPlaces": 2
}
  }
}

Chain multiple tools in one session with a comma-separated toolId list, e.g. /mcp/sse?toolId=png-to-webp,jpg-to-webp,gif-to-webp (max 20).

Questions or issues? Contact [email protected]

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Name

Type

Required

Description

number

Yes

Population size at t = 0 (cells, individuals, biomass — any unit).

number

Yes

Constant per-capita rate: r > 0 growth, r < 0 decline, r = 0 stationary.

number

Yes

Time elapsed in the same unit as r.

decimalPlaces

number

—

{ "mcpServers": { "elysiatools-exponential-growth-population": { "name": "exponential-growth-population", "description": "Compute N_t = N₀·e^(rt) with fold change, doublings, doubling time, or half-life.", "baseUrl": "https://api.elysiatools.com/mcp/sse?toolId=exponential-growth-population", "command": "", "args": [], "env": {}, "isActive": true, "type": "sse" } } }

{ "jsonrpc": "2.0", "id": 2, "method": "tools/call", "params": { "name": "exponential-growth-population", "arguments": { "n0": 1000, "r": 0.4, "t": 10, "decimalPlaces": 2 } } }