Build a function from context by determining an explicit formula, recursive rule, or calculation process.
Build an explicit linear function from a starting value and constant rate
Problem
A plant starts at \(6~\text{centimeters}\) and grows \(2~\text{centimeters}~\text{each}~\text{week}\). Write an explicit linear function for its height and define the variables.
Big Picture
What this problem is really about
A constant-rate model combines what is already present with the change accumulated over the input interval. We’ll define the time input and measured output, place the time-zero value as the constant term, and multiply the signed rate by elapsed time. Checks at zero and one time unit reveal whether the start, rate, sign, and units were assigned correctly.
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