The function \(\mathrm{f(x) = 55.20 - 0.16x}\) gives the estimated surface water temperature \(\mathrm{f(x)}\), in degrees Celsius, of a body...

1. TRANSLATE the problem information

• Given information:
  • Function: \(\mathrm{f(x) = 55.20 - 0.16x}\)
  • Domain: \(\mathrm{220 \leq x \leq 360}\)
  • Need to find: temperature on the 326th day

• What this tells us: We need to evaluate \(\mathrm{f(326)}\)

2. SIMPLIFY through substitution and calculation

• Substitute \(\mathrm{x = 326}\) into the function:
  \(\mathrm{f(326) = 55.20 - 0.16(326)}\)

• Calculate the multiplication: \(\mathrm{0.16 \times 326 = 52.16}\)

• Complete the subtraction: \(\mathrm{f(326) = 55.20 - 52.16 = 3.04}\)

Answer: B. 3.04

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students may not recognize that "temperature on the 326th day" means they need to substitute 326 for x in the function. They might think the answer is just one of the given coefficients or constants.

This may lead them to select Choice A (55.20) by taking just the constant term, or Choice C (-0.16) by taking just the coefficient.

Second Most Common Error:

Poor SIMPLIFY execution: Students correctly identify they need \(\mathrm{f(326)}\) but make arithmetic errors. The most likely error is calculating \(\mathrm{-0.16(326) = -52.16}\) and stopping there, forgetting to add the 55.20.

This may lead them to select Choice D (-52.16).

The Bottom Line:

This problem tests whether students understand function notation and can execute multi-step arithmetic accurately. The key insight is recognizing that finding the temperature "on the 326th day" means evaluating the function at \(\mathrm{x = 326}\).