A function p estimates that there were 2,000 animals in a population in 1998 . Each

Choice C is correct. It's given that a function $p$ estimates that there were $\mathrm{2,000}$ 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 $\mathrm{2,000}$ for $a$ and $3$ for $r$ in this function yields $p\left(x\right)=\mathrm{2,000}{\left(1+\frac{3}{100}\right)}^x$, or $p\left(x\right)=\mathrm{2,000}{\left(1.03\right)}^x$.

Choice A is incorrect. This function represents a population in which each year the number of animals increased by $200\%$, not $3\%$, of the number of animals in the population the previous year.

Choice B is incorrect. This function represents a population in which each year the number of animals increased by $97\%$, not $3\%$, of the number of animals in the population the previous year.

Choice D is incorrect. This function represents a population in which each year the number of animals decreased, rather than increased, by $3\%$ of the number of animals in the population the previous year.