A biologist modeled the mass y, in grams, of a bacterial... | SAT Two-variable data: models and scatterplots Question, Answer Explained

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Math · Problem-Solving and Data AnalysisHard

A biologist modeled the mass $y$ , in grams, of a bacterial culture $x$ days after the start of an experiment with an exponential function of the form $y = a(b)^x$ , where $a$ and $b$ are positive constants. The model predicts a mass of $60$ grams after $1$ day and $86.4$ grams after $3$ days. What is the value of $a$ ?

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Answer: 50

From day $1$ to day $3$ , the mass is multiplied by $b$ twice, so $b^2 = \frac{86.4}{60} = 1.44$ and $b = 1.2$ . Then $a(1.2)^1 = 60$ , so $a = \frac{60}{1.2} = 50$ .

Using $60$ as the value of $a$ is incorrect because $a$ is the mass at $x = 0$ , not at $x = 1$ .

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