Question 5 of 9, Step 1 of 1 Growing linearly, the balance owed on your credit card doubles from $$ \$ 700 $$ to $$ \$ 1400 $$ in 6 months. If the balance were growing according to the exponential function $$ f(x)=700(1+0.122)^{x} $$ where $$ x $$ represents the number of months, what would the balance be after 6 months? Round your answer to the nearest cent. Answer How to enter your answer (opens in new window) Keyboard Shortcuts

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To determine the balance after 6 months using the exponential growth model $$ f(x) = 700(1 + 0.122)^x $$, where $$ x $$ represents the number of months, follow these steps:

1. **Identify the Variables:**
   - Initial balance: \$700
   - Growth rate per month: 12.2% or 0.122
   - Number of months: 6

2. **Plug the Values into the Exponential Function:**
   $$
   f(6) = 700 \times (1 + 0.122)^6
   $$
   $$
   f(6) = 700 \times 1.122^6
   $$

3. **Calculate $$ 1.122^6 $$:**
   $$
   1.122^6 \approx 1.995
   $$
   *(This can be calculated using a calculator or exponential functions.)*

4. **Multiply by the Initial Balance:**
   $$
   f(6) = 700 \times 1.995 \approx 1,396.50
   $$

5. **Final Answer:**
   $$
   \boxed{\$1,\!396.50}
   $$
After 6 months, the balance would be \$1,396.50.

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