Problem

Compare the \(\text{two}~\text{payment}~\text{plans}\) after \(6~\text{weeks}\). Evaluate Plan A as \(500+25(6)\), evaluate Plan B by computing \(2^6\) before multiplying by \(100\), and base the decision on the \(\text{two}~\text{dollar}~\text{amounts}\).

Big Picture

What this problem is really about

A decision context fixes the comparison horizon and units before model type matters. We’ll translate each plan into its correct linear or exponential expression, evaluate both at the same time, and compare the resulting amounts in common units.

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Plan B is better because after 6 weeks, 100·2⁶ = 6400 while 500 + 25·6 = 650.

Plan A is better because after 6 weeks, 500 + 25·6 = 650 while Plan B is only 100 + 2·6 = 112.

Plan A is better because after 6 weeks, 500 + 25·6 = 650 while Plan B is 100·6 = 600.

Plan A is better because Plan B only doubles 6 times to 64, and 64 is less than 650.

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Compare the \(\text{two}~\text{payment}~\text{plans}\) after \(6~\text{weeks}\). Evaluate Plan A as \(500+25(6)\), evaluate Plan B by computing \(2^6\) before multiplying by \(100\), and base the decision on the \(\text{two}~\text{dollar}~\text{amounts}\).

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