Problem
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. Answer How to enter your answer (opens in new window) Keypad Keybo ard Shortcuts $\$$
Solution
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.
