Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Choose whether a context is modeled by a quadratic or an exponential function
Problem
Classify rectangle area formed from \(\text{two}\) side lengths that are each linear in \(x\). Write the generic product \((ax+b)(cx+d)\), identify its highest power after expansion, and contrast this structure with repeated percent change.
Big Picture
What this problem is really about
The location of the variable determines the function family more reliably than the mere presence of multiplication. We’ll represent both changing sides as linear expressions, expand their one-time area product to identify its highest power, and contrast that polynomial structure with repeated factor change that places the input in an exponent.
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