Estimation question

Estimate the compute cost of giving every X user free access to Grok.

Practice this question out loud. An AI interviewer asks it, follows up like a real interviewer would, and scores your answer. Type or speak.

What this question tests

Estimation combining a massive user base with realistic engagement assumptions to avoid wild overestimation.

State assumptions: assume X has roughly 250 million monthly active users, but only a fraction would actively use a free Grok feature regularly.
Estimate active Grok users: assume 10 percent of monthly actives try it in a given month, and of those, 30 percent use it weekly, giving roughly 7.5 million weekly active Grok users.
Estimate queries per user: assume an average of 3 queries per weekly active user per week.
Estimate cost per query: assume a blended inference cost of roughly 0.01 dollars per query for a mixed-size model serving free users.
Multiply: 7.5 million users times 3 queries times an assumed 0.01 dollars equals roughly 225,000 dollars per week, or roughly 32,000 dollars per day, clearly marked as a rough estimate.

Builds from a realistic adoption funnel, monthly actives down to weekly active Grok users, rather than assuming all 250 million users query it constantly.
States the per-query cost assumption explicitly and notes it would rise sharply if usage skewed toward longer, more complex queries.
Shows clean arithmetic to a final daily or weekly cost figure, explicitly labeled as an order-of-magnitude estimate.
Notes the result is highly sensitive to the adoption-rate assumption, and flags that as the biggest uncertainty in the whole estimate.

Assuming all 250 million monthly active X users query Grok daily, which wildly overstates realistic free-feature adoption.
Skipping the cost-per-query assumption and jumping straight to a headline number without showing the reasoning.

How would this estimate change if Grok became the default response to every X search query?
What is the biggest cost lever xAI could pull to make free access sustainable at scale?