Choose the best answer to the following question. Explain your reasoning with on
ID: 3121631 • Letter: C
Question
Choose the best answer to the following question. Explain your reasoning with one or more complete sentences. The balance owed on your credit card doubles from $1000 to $2000 in 6 months. If your balance growing exponentially, how much longer will it be until it reaches $4000? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. It will be 12 months because the balance increases by $1500 every 6 months. B. It will be 6 months because the balance doubles every 6 months, and $4000 is twice as much as $2000. C. It will be 18 months because $1000 has to double three times to become $4000. D. It will be 18 months because the balance increases by $1000 every 6 months, and $4000 is $3000 more than $1000. E. It will be 6 months because the balance increases by $2000 every three months. F. It will be 12 months because it takes 6 months to $2000 and another 6 months to reach $4000.Explanation / Answer
Option F
Dear Student Thank you for using Chegg !! Given that the balance owned by credit card doubles in 6 months Let the exponential function be P = P0 (2)^(kt) p : Present Balance of credit card P0 : Initial Balance of Credit Card k : Rate of increase t : Time period (years) Given P0 = 1000 $ P( 6 months) = 2000 $ t = 0.5 years => 2000 = 1000 (2)^(0.5k) 2 = 2^(0.5k) => k = 2 Now when credit card balance is 4000 i.e. P = 4000, time elapsed ?? 4000 = 1000 (2)^(2t) 4 = 4^t t = 1 year Solution