Compare growth of exponential, linear, quadratic, and other polynomial models using graphs/tables.
Separate initial value from growth behavior
Problem
Compare \(A(t)=100(1.10)^t\) and \(B(t)=250(1.10)^t\) by separating each initial value from the shared multiplier. State \(\text{both}~\text{values}\) at \(t=0\), convert \(1.10\) to a percent growth rate, and simplify \(B(t)/A(t)\) to show the relationship for every \(t\).
Big Picture
What this problem is really about
A larger output can come from a larger starting value without implying a faster growth rate. We’ll evaluate both models at zero, interpret their shared multiplier, and simplify a same-input output ratio to separate initial scale from growth behavior.
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