Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint, idempotentHint, openWorldHint and destructiveHint=false, so the safety profile is covered structurally. The description adds two pieces of real value beyond that: the growth model used and a 'cost: 1 credit' billing note. It does not mention that the projection assumes a fixed rate and ignores migration/fertility dynamics, which is the main behavioral caveat.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Is the description appropriately sized, front-loaded, and free of redundancy?

A single front-loaded sentence that names the computation and its model, with the credit cost appended. No wasted wording, though it is terse enough that the assumptions of the model go unstated.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

For a simple three-parameter deterministic math function with full schema coverage, rich safety annotations and no output schema, nothing an agent needs in order to call it correctly is missing. The model name and credit cost make it self-sufficient.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%, so num_years, current_pop and annual_growth are fully documented in the schema, including the percentage convention. The description only echoes the percentage convention and adds no unit, range, or input-format detail beyond it; baseline 3 applies.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Does the description clearly state what the tool does and how it differs from similar tools?

States a specific verb and resource ('Projects future population size') and names the underlying model ('exponential growth formula with a constant annual growth rate'), which separates it from generic calculators like compound_interest or average. It does not explicitly name a sibling to avoid, so it stops short of the top score.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Does the description explain when to use this tool, when not to, or what alternatives exist?

No explicit when-to-use or when-not-to-use guidance and no named alternative among the many math siblings (project_investment_growth, calculate_bacterial_growth). The 'constant annual growth rate' phrasing implicitly signals the model's assumption, which is the only usage hint provided.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.