A company opens an account with an initial balance of $\$\mathrm{36,100.00}$. The account earns interest, and no additional deposits or withdrawals are made. The account balance is given by an exponential function $A$, where $A\left(t\right)$ is the account balance, in dollars, $t$ years after the account is opened. The account balance after $13$ years is $\$\mathrm{68,071.93}$. Which equation could define $A$?