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Which of the following scatterplots shows a relationship that is appropriately modeled with the equation y=ax^(b) , where a is positive and b is negative?

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Solution :The graph of `y = a x ^(b)` , where a is positive and b is NEGATIVE, has a positive y-intercept and rapidly decreases (in PARTICULAR, decreases at a faster rate than a linear function) toward the x-axis as x increases. Of the scatterplots shown, only the ONE in choice B would be APPROPRIATELY modeled by such a function.
Choice A is incorrect, as this scatterplot is appropriately modeled by a linear function. Choice C is incorrect, as this scatterplot is appropriately modeled by an increasing function.Choice D is incorrect, as this scatterplot shows no clear relationship between x and y.


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