Cost Forecast
Budgeting a Long Session
Library › Context Problems
One turn's input grows by a fixed step, so the tenth turn sends ten times what the first did. That much is a straight line. But the bill is not the last turn, it is every turn added together, and adding up a straight line gives a curve. That is why doubling the length of a conversation does not double what it costs to run, it roughly quadruples it. The output never joins that curve. It is the same size every turn, so adding it up stays a straight line, and the input half of the bill runs away from it however dearly the output is priced.
