SAT Question dbd89c59: Two-variable Data Models And Scatterplots answer and explanation with Desmos solution

Choice B is correct. It’s given that the scatterplot shows the relationship between the number of swans, $y$, and the number of years since $1970$, $x$, where $0\le x\le 50$. According to the scatterplot, the number of swans increases as the number of years since $1970$ increases, and the data shows an exponential growth pattern rather than a linear pattern. When $a>0$ and $b>1$, an exponential model of the form $y=a(b{)}^x$ represents exponential growth and a model of the form $y=a{\left(b\right)}^{-x}$ represents exponential decay. The models in all four choices show $a>0$ and $b>1$. Choices B and D show models of the form $y=a(b{)}^x$ and thus represent exponential growth. The initial value $a$ should approximate the y-value when $x=0$, which is a little more than $40$, so $a=43$ is reasonable and consistent with the graph. Therefore, the equation $y=43(1.04{)}^x$ is the most appropriate exponential model for the data.