A model of how AI agent token usage scales across two independent axes: task horizon (how long the agent works) and goal direction (how the agents are orchestrated). Each axis has a distinct scaling regime — and they multiply together.
Model notes. Baseline calibrated to 1M tokens/day at H=1, G=1. H scales as a power law (H^1.67) reflecting superlinear context accumulation over longer task horizons. G uses piecewise log-linear interpolation between empirically anchored points (G=1→1×, G=4→10×, G=5→50×, G=7→100×, G=10→10,000×) reflecting discrete phase transitions between orchestration, hierarchical, and recursive agent architectures. Cost estimate uses Sonnet 4.5 blended input/output pricing (~$3/MTok). Model is illustrative; real consumption varies by task type, prompt design, and caching strategy. · Exponential View