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. Quns

To find the balance after 6 months using the given exponential function \( f(x) = 700(1 + 0.122)^{x} \), simply substitute \( x \) with 6: \[ f(6) = 700(1 + 0.122)^{6} = 700(1.122)^{6} \] Calculating \( (1.122)^{6} \) gives approximately 1.8994. Now multiply this by 700: \[ f(6) \approx 700 \times 1.8994 \approx 1329.58 \] Thus, rounding to the nearest cent, the balance would be approximately \( \$1329.58 \). Now you have your answer for the balance after 6 months, so make sure to keep track of those credit card charges! Remember, an exponential growth in debt can sneak up on you faster than you'd think!