The balance owed on your credit card triples from $\$ 600$ to $\$ 1800$ in 12 months, If the balance is growing linearly then it would take 64 months to reach $\$ 7000$. If, on the other hand, the balance is growing exponentially, $f(x)=600(1+0.096)^{x}$ where $x$ represents the number of months, what would the balance be after 64 months? Round your answer to the nearest cent.
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\(\boxed{\$211849.15}\) is the final answer.
Step 1 ：Let's substitute $x=64$ into the function $f(x)=600(1+0.096)^{x}$ to find the balance after 64 months.
Step 2 ：So, the balance after 64 months is $600(1+0.096)^{64}$ = 211849.14514760638.
Step 3 ：Rounding to the nearest cent, the balance after 64 months would be $\$211849.15$.
Step 4 ：\(\boxed{\$211849.15}\) is the final answer.
