Question:The function g is defined by \(\mathrm{g(t) = 2t(t + 7)}\). What is the value of \(\mathrm{g(5)}\)?245060120

1. TRANSLATE the problem instruction

• We need to find \(\mathrm{g(5)}\), which means we substitute \(\mathrm{t = 5}\) into the function \(\mathrm{g(t) = 2t(t + 7)}\)
• This gives us: \(\mathrm{g(5) = 2(5)(5 + 7)}\)

2. SIMPLIFY the expression step by step

• First, evaluate what's in parentheses: \(\mathrm{5 + 7 = 12}\)
• Now we have: \(\mathrm{g(5) = 2(5)(12)}\)
• Next, multiply from left to right: \(\mathrm{2(5) = 10}\)
• Finally: \(\mathrm{10 \times 12 = 120}\)

Answer: D

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak SIMPLIFY execution: Students make arithmetic errors during the multi-step calculation process.

Common mistakes include:

• Incorrectly adding 5 + 7 (getting 11 instead of 12)
• Making errors when multiplying 2 × 5 × 12 in sequence
• Forgetting to follow order of operations and multiplying in wrong order

For example, if they incorrectly compute \(\mathrm{5 + 7 = 11}\), they would get \(\mathrm{g(5) = 2(5)(11) = 110}\), but this isn't among the choices, leading to confusion and guessing.

The Bottom Line:

This is a straightforward substitution problem where success depends entirely on careful arithmetic execution. The function evaluation concept is simple, but computational accuracy determines whether students select the correct answer.