Question

1. use patterns and 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: Calculate doubling - times

The money doubles every 8 years. For 48 years, the number of 8 - year intervals is $\frac{48}{8}=6$.

Step2: Analyze the expression

The initial investment is $1$. Since the money doubles 6 times, the amount of money in the account after 48 years is $1\times2\times2\times2\times2\times2\times2 = 2^6$. Each multiplication by 2 represents a doubling of the money.

Answer:

Yes, the expression $1\times2\times2\times2\times2\times2\times2$ correctly represents how much is in the investment account after 48 years because the money doubles 6 times in 48 years (as $48\div8 = 6$), and each doubling is represented by a multiplication by 2.