A scatterplot shows the amount y, in milligrams, of a... | SAT Two-variable data: models and scatterplots Question, Answer Explained

Question bank / Two-variable data: models and scatterplots

Math · Problem-Solving and Data AnalysisMedium

A scatterplot shows the amount $y$ , in milligrams, of a medication in a patient's bloodstream $x$ hours after a dose. The values of $y$ decrease quickly at first and then more slowly, getting closer and closer to $0$ without reaching it. Which of the following equations could best model the data?

$y = 120 - 15x$

$y = 120(1.6)^x$

$y = 15x + 120$

$y = 120(0.6)^x$

Show answer and explanation

Answer: D

Values that fall quickly at first, then more slowly, while approaching $0$ fit exponential decay, $y = a(b)^x$ with $0 < b < 1$ . Choice D has $b = 0.6$ , so each hour the amount is multiplied by $0.6$ . Choices B and C increase, and choice A decreases by the same amount every hour.

Choice A decreases, but a linear model drops by the same $15$ milligrams every hour and reaches $0$ after $8$ hours, which doesn't match the data.

Why the other choices are wrong

A. This linear model drops by 15 milligrams every hour and reaches 0 after 8 hours, but the data level off.
B. A base greater than 1 gives exponential growth, but the data decrease.
C. This linear model increases, but the data decrease.

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