The sterplot has 6 data points. The data points are in an exponential pattern trending down from left to right.

Question

The sterplot 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 $b$ ?

Accepted Answer

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.

Question the-st