SAT Question 7a4475df: Nonlinear Functions answer and explanation with Desmos solution

Choice C is correct. It's given that a function $p$ estimates that there were $2,000$ animals in a population in $1998$ and that each year from $1998$ to $2010$, the number of animals in this population increased by $3\%$ of the number of animals in the population the previous year. It follows that this situation can be represented by the function $p\left(x\right)=a{\left(1+\frac{r}{100}\right)}^x$, where $p\left(x\right)$ is the estimated number of animals in the population $x$ years after $1998$, $a$ is the estimated number of animals in the population in $1998$, and each year the estimated number of animals increased by $r\%$. Substituting $2,000$ for $a$ and $3$ for $r$ in this function yields $p\left(x\right)=2,000{\left(1+\frac{3}{100}\right)}^x$, or $p\left(x\right)=2,000{\left(1.03\right)}^x$.