Growing linearly, the balance owed on your credit card triples from $\$ 700$ to $\$ 2100$ in 12 months. If the balance were growing according to the exponential function $f(x)=700(1+0.096)^{x}$ where $x$ represents the number of months, what would the balance be after 12 months? Round your answer to the nearest cent.
Answer
\(\boxed{2102.93}\) is the balance after 12 months, if it were growing according to the given exponential function.
Step 1 ：Substitute $x=12$ into the function $f(x)=700(1+0.096)^{x}$ to find the balance after 12 months.
Step 2 ：Calculate the balance: $f(12)=700(1+0.096)^{12}=2102.9293859167524$
Step 3 ：Round the balance to the nearest cent: $\$2102.93$
Step 4 ：\(\boxed{2102.93}\) is the balance after 12 months, if it were growing according to the given exponential function.
