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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Hard

The scatterplot shows the relationship between two variables, $x$ and $y$ . An equation for the exponential model shown can be written as $y = a {(b)}^{x}$ , where $a$ and $b$ are positive constants. Which of the following is closest to the value of $b$ ?

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Explanation

Choice A is correct. It's given that an equation for the exponential model shown can be written as $y = a {(b)}^{x}$ , where $a$ and $b$ are positive constants. For an exponential model written in this form, if the value of $b$ is greater than $0$ but less than $1$ , the model is decreasing. If the value of $b$ is greater than $1$ , the model is increasing. The exponential model shown is decreasing. Therefore, the value of $b$ is greater than $0$ but less than $1$ . Of the given choices, only $0.83$ is a value greater than $0$ but less than $1$ . Thus, $0.83$ is closest to the value of $b$ .

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

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

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