A function $p$ estimates that there were $\mathrm{2,000}$ animals in a population in $1998$. Each year from $1998$ to $2010$, the function estimates that the number of animals in this population increased by $3\%$ of the number of animals in the population the previous year. Which equation defines this function, where $p\left(x\right)$ is the estimated number of animals in the population $x$ years after $1998$?