Let's simplify the given expression step-by-step to find the equivalent expression.
The original expression is:
[tex]\[ 6 \cdot (1 + 0.40)^{2x} \][/tex]
First, we simplify inside the parentheses:
[tex]\[ 1 + 0.40 = 1.40 \][/tex]
So, the expression becomes:
[tex]\[ 6 \cdot (1.40)^{2x} \][/tex]
Next, we recognize that we can rewrite [tex]\((1.40)^{2x}\)[/tex] as:
[tex]\[ (1.40)^{2x} = ((1.40)^2)^x \][/tex]
Calculating [tex]\((1.40)^2\)[/tex]:
[tex]\[ (1.40)^2 = 1.96 \][/tex]
Therefore, the expression simplifies to:
[tex]\[ 6 \cdot (1.96)^x \][/tex]
So, the equivalent expression is:
[tex]\[ 6 \cdot (1.96)^x \][/tex]
The correct answer is:
[tex]\[ 6 \cdot (1.96)^x \][/tex]
