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Algebra / Linear functions Difficulty: Easy

In science class, Diego conducted an experiment to learn about evaporation. Diego measured the height of fluid in a beaker over a period of time. The function $f (x) = 39 - 0.18 x$ gives the estimated height, $in centimeters (cm)$ , of the fluid in the beaker $x$ days after the start of the experiment. Which of the following is the best interpretation of $39$ in this context?

The estimated height, $in cm$ , of the fluid at the start of the experiment

The estimated height, $in cm$ , of the fluid at the end of the experiment

The estimated change in the height, $in cm$ , of the fluid each day

The estimated number of days for all the fluid to evaporate

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Explanation

Choice A is correct. It’s given that the function $f (x) = 39 - 0.18 x$ gives the estimated height, in centimeters (cm), of the fluid in the beaker $x$ days after the start of the experiment. For a function defined by an equation of the form $f (x) = b + m x$ , where $m$ and $b$ are constants, $b$ represents the value of $f (x)$ when $x equals 0$ . It follows that in the given function, $39$ represents the value of $f (x)$ when $x equals 0$ . Since $x equals 0$ represents the start of the experiment, then the best interpretation of $39$ in this context is that the estimated height, in cm, of the fluid was $39$ at the start of the experiment.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect. The estimated change in the height, in cm, of the fluid each day is $0.18$ , not $39$ .

Choice D is incorrect and may result from conceptual errors.