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Algebra Difficulty: Medium

The function $f (x) = 55.20 - 0.16 x$ gives the estimated surface water temperature $f (x)$ , in degrees Celsius, of a body of water on the $x th$ day of the year, where $220 \leq x \leq 360$ . Based on the model, what is the estimated surface water temperature, in degrees Celsius, of this body of water on the $326th$ day of the year?

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Explanation

Choice B is correct. It’s given that the function $f (x) = 55.20 - 0.16 x$ gives the estimated surface water temperature, in degrees Celsius, of a body of water on the $x th$ day of the year. Substituting $326$ for $x$ in the given function yields $f (326) = 55.20 - 0.16 (326)$ , which is equivalent to $f (326) = 55.20 - 52.16$ , or $f left parenthesis 326 right parenthesis equals 3.04$ . Therefore, the estimated surface water temperature, in degrees Celsius, of this body of water on the $326th$ day of the year is $3.04$ .

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect. This is the rate of change, in degrees Celsius per day, of the estimated surface water temperature.

Choice D is incorrect. This is the change, in degrees Celsius, in the estimated surface water temperature over $326$ days.