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Algebra / Linear functions Difficulty: Easy

As part of a science project on evaporation, Amaya measured the height of a liquid in a container over a period of time. The function $f (x) = 33 - 0.18 x$ gives the estimated height, in centimeters (cm), of the liquid in the container $x$ days after the start of the project. Which of the following is the best interpretation of $33$ in this context?

The estimated height, in cm, of the liquid at the start of the project

The estimated height, in cm, of the liquid at the end of the project

The estimated change in the height, in cm, of the liquid each day

The estimated number of days for all of the liquid to evaporate

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Explanation

Choice A is correct. It's given that the function $f (x) = 33 - 0.18 x$ gives the estimated height, in centimeters (cm), of the liquid in the container $x$ days after the start of the project. For a linear function in the form $f (x) = a + b x$ , where $a$ and $b$ are constants, $a$ represents the value of $f left parenthesis 0 right parenthesis$ and $b$ represents the rate of change of the function. It follows that in the given function, $33$ represents the value of $f left parenthesis 0 right parenthesis$ . Therefore, the best interpretation of $33$ in this context is the estimated height, in cm, of the liquid at the start of the project.

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

Choice C is incorrect. The estimated change in the height, in cm, of the liquid each day is $0.18$ , not $33$ .

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