Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Build a recursive exponential model from a context
Problem
Write a zero-based recursive model for a population starting at \(200\) and doubling each generation. Define \(P(0)\), give \(P(n)\) in terms of \(P(n-1)\) with \(n\ge~1\), and generate the first \(\text{two}\) new generations as a check.
Big Picture
What this problem is really about
A recursive exponential model needs both an indexed starting value and a rule that multiplies the preceding term. We’ll place the initial population at generation zero, translate doubling into a constant factor on the previous generation, specify where the recurrence begins, and generate the next two terms as a check.
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