The balance owed on your credit card doubles from $\$ 800$ to $\$ 1600$ in 6 months. If the balance is growing linearly then it would take 61.5 months to reach $\$ 9000$. If, on the other hand, the balance is growing exponentially, $f(x)=800(1+0.122)^{x}$ where $x$ represents the number of months, what would the balance be after 61.5 months? Round your answer to the nearest cent.

Step 1 ：Given the exponential growth function \(f(x)=800(1+0.122)^{x}\), where \(x\) represents the number of months.

Step 2 ：Substitute \(x=61.5\) into the function to find the balance after 61.5 months.

Step 3 ：Calculate the result to get the balance: \(f(61.5)=800(1+0.122)^{61.5}=949840.5091231895\).

Step 4 ：Round the balance to the nearest cent to get \$949840.51.

Step 5 ：Final Answer: The balance after 61.5 months would be approximately \(\boxed{949840.51}\).