Build a function from context by determining an explicit formula, recursive rule, or calculation process.
Critique and correct a proposed function model
Problem
The proposed model \(C(m)~=~20m~+~5\) is meant to represent a \(\$20\) starting fee plus \(\$5~\text{per}~\text{month}\). Correct the model and identify the error.
Big Picture
What this problem is really about
A proposed model should be tested against structural facts in the context, not accepted from its appearance. We’ll evaluate it at zero to test the one-time fee, compare outputs one month apart to test the rate, and check the units assigned to each term. Any failed test identifies which parameter roles must be corrected before the revised model is verified again.
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