SAT Question fb866265: Two-variable Data Models And Scatterplots answer and explanation with Desmos solution

Choice A is correct. It's given that an equation for the exponential model shown can be written as $y=a{\left(b\right)}^x$, 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 $b$.