Question

1. use structure an investment of $1 was put in an account. every 8 years, the money doubled. no additional money was added to the account. would the expression 1 × 2 × 2 × 2 × 2 × 2 × 2 correctly represent how much was in the investment account after 48 years? explain.

Explanation:

Step1: Determine the number of doubling periods

We know that the money doubles every 8 years, and we want to find out how much is in the account after 48 years. To find the number of doubling periods, we divide the total number of years (48) by the number of years per doubling period (8). So, \( \frac{48}{8} = 6 \). This means the money doubles 6 times.

Step2: Analyze the growth of the investment

The initial investment is $1. Each time it doubles, we multiply the current amount by 2. After the first 8 years, it becomes LXI0. After the second 8 years (16 years total), it becomes LXI1, and so on. Since it doubles 6 times, the amount in the account after 48 years is LXI2, which is LXI3 (or LXI4). Calculating LXI5, we know that LXI6. So the expression LXI7 (or LXI8) correctly represents the amount in the investment account after 48 years because we start with $1 and double it 6 times (once every 8 years for 48 years).

Answer:

The expression \( 1\times2\times2\times2\times2\times2\times2 \) (or \( 2^6 \)) is correct because the investment of $1 doubles every 8 years, and over 48 years, it doubles LXI2 times, so we multiply the initial $1 by 2 six times. The amount in the account after 48 years is \( \$64 \).