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A company opens an account with an initial balance of $35,600.00. The account earns interest, and no additional deposits or withdrawals are made. The account balance is given by an exponential function $A$, where $A(t)$ is the account balance, in dollars, $t$ years after the account is opened. The account balance after $15$ years is $129,672.38. Which equation could define $A$?

A

$A(t)=35,600.00(1.09{)}^t$

B

$A(t)=35,600.00(0.09{)}^t$

C

$A(t)=94,072.38(1.09{)}^t$

D

$A(t)=94,072.38(0.09{)}^t$