SAT Question c048055c: Nonlinear Functions answer and explanation with Desmos solution

Choice D is correct. It's given that a model predicts the population of Bergen in $2005$ was $15,000$. The model also predicts that each year for the next $5$ years, the population increased by $4\%$ of the previous year's population. The predicted population in one of these years can be found by multiplying the predicted population from the previous year by $1.04$. Since the predicted population in $2005$ was $15,000$, the predicted population $1$ year later is $15,000(1.04)$. The predicted population $2$ years later is this value times $1.04$, which is $15,000\left(1.04\right)\left(1.04\right)$, or $15,000{\left(1.04\right)}^2$. The predicted population $3$ years later is this value times $1.04$, or $15,000{\left(1.04\right)}^3$. More generally, the predicted population, $p$, $x$ years after $2005$ is represented by the equation $p=15,000{\left(1.04\right)}^x$.