Interpret terms, factors, and coefficients in quadratic and exponential expressions.
Distinguish additive, power, and multiplicative growth
Problem
Compare \(S(t)=500+30t\) and \(E(t)=500(1.06)^t\). For each model, identify its structure, evaluate the initial value, describe additive or multiplicative change per step, and classify the function family.
Big Picture
What this problem is really about
The two models can share an initial value while following fundamentally different change rules. We’ll locate where the variable appears, evaluate each model at zero, and compare a constant added difference with a constant multiplicative ratio to classify each structure.
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