Answered

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Which of the following is an equivalent expression to [tex]$6 \cdot(1+0.40)^{2x}$[/tex]?

A. [tex]6 \cdot(2.8)^x[/tex]
B. [tex]6 \cdot(1.96)^x[/tex]
C. [tex]36 \cdot(1.4)^x[/tex]
D. [tex]12 \cdot(1.4)^x[/tex]

Sagot :

GinnyAnswer
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]
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