EI-201c · Module 2

Trajectory Extrapolation

3 min read

Trajectory extrapolation projects the current direction and velocity of an ecosystem trend into the future. If model inference costs have declined 40% per quarter for four consecutive quarters, extrapolation projects continued decline — and calculates when the cost crosses thresholds that enable new use cases. The method is simple: plot historical data, identify the trend line, and project forward. The challenge is knowing when the trend line will break — when a force reversal, a ceiling effect, or a structural change alters the trajectory.

Do This

  • Plot at least 4 data points before extrapolating — fewer than 4 is fitting a line to noise
  • Identify ceiling and floor effects — some metrics cannot continue declining or growing indefinitely
  • State your extrapolation assumptions explicitly — "assuming no regulatory intervention and continued GPU supply growth"
  • Update trajectories quarterly with new data — extrapolation accuracy degrades over time without refreshes

Avoid This

  • Assume exponential trends continue indefinitely — every exponential curve eventually encounters a constraint
  • Extrapolate from cherry-picked time periods — the last 3 months may not represent the structural trend
  • Present extrapolation as prediction — extrapolation is a projection of current trends, not a forecast of future reality

The most valuable application of trajectory extrapolation is threshold analysis. At the current rate of cost decline, when does inference become cheap enough to power always-on AI assistants? At the current rate of capability improvement, when does the open-source frontier reach proprietary parity on enterprise benchmarks? These threshold crossings are decision points. Knowing when they arrive — even approximately — is the strategic value of extrapolation.