Question

The balance owed on your credit card doubles from $500 to $1000 in 6 months. If your balance is growing exponentially, how much longer will it be until it reaches $2000?

A. It will be 6 months because the balance increases by $1000 every three months.
B. It will be 12 months because it takes 6 months to reach $1000 and another 6 months to reach $2000.
C. It will be 18 months because the balance increases by $500 every 6 months, and $2000 is $1500 more than $500
D. It will be 18 months because $500 has to double three times to become $2000.
E. It will be 12 months because the balance increases by $750 every 6 months.
F. It will be 6 months because the balance doubles every 6 months, and $2000 is twice as much as $1000

Answer 1

Since the balance is growing exponentially and doubles every 6 months, it will take the same amount of time for the balance to double from $1000 to $2000, which is also 6 months.

The correct answer is F. It will be 6 months because the balance doubles every 6 months, and $2000 is twice as much as $1000

How much longer will it be until it reaches $2000?

When the balance on the credit card doubles from $500 to $1000 in 6 months, we can observe that the balance is growing exponentially. This means that the balance is increasing by a certain factor over a given time period.

In this case, the balance doubled in 6 months, indicating that the growth factor is 2. This means that every 6 months, the balance on the credit card doubles.

Now, if we want to determine how much longer it will take for the balance to reach $2000, analyze the growth pattern.

Since the balance doubles every 6 months, it will take another 6 months for the balance to double from $1000 to $2000.