Question

Money that is collecting interest in a bank account

doubles in value every 8 years.
When the account was opened, it had 8, or 2³,
dollars in it. After 32 years, the account balance
has doubled 4 times, increasing by a factor of 24
It now has a balance of 2³.2¹. Expressed as a
power, how much money, in dollars, is in the
account after 32 years?

Answer 1

Explanation:

The initial balance of the account was 8 dollars, which is equal to 2³ (2 raised to the power of 3).

After 32 years, the account balance has doubled 4 times, increasing by a factor of 2^4 (2 raised to the power of 4).

Therefore, the final balance after 32 years can be calculated as:

Final balance = Initial balance * (2^4)

Final balance = 2³ * (2^4)

Final balance = 2^(3+4)

Final balance = 2^7

Expressed as a power, the amount of money in the account after 32 years is 2^7. This is equivalent to 128 dollars.