Question

Which two expressions are equivalent?A. A(0.52)-21B. A(1.04)-C. A(0.96)D. A(0.96 0.08

Answer 1

Equivalent expressions are expressions that have the values when we put the same values for the variables.

From the given expressions, let's find the equivalent expressions.

From the given expressions, let's substitute 1 for t and evaluate.

The expressions with the same result will be equivalent expressions.

`\begin{gathered} A(0.52)^(-2t) \\ \\ A(0.52)^(-2(1)) \\ \\ A(0.52)^(-2) \\ \\ A((1)/(0.52^2)) \\ \\ A((1)/(0.274)) \\ \\ =3.698A \end{gathered}`
`\begin{gathered} A(1.04)^(-t)_{} \\ \\ A(1.04)^(-1) \\ \\ A((1)/(1.04)) \\ \\ A(0.96) \\ \\ =0.96A \end{gathered}`
`\begin{gathered} A(0.96)^t \\ \\ A(0.96)^1 \\ \\ A(0.96) \\ \\ =0.96A \end{gathered}`
`\begin{gathered} A(0.96)^(0.08t)^{} \\ \\ A(0.96)^(0.08(1)) \\ \\ A(0.96)^(0.08) \\ \\ A(0.998) \\ \\ =0.998A \end{gathered}`

The expressions with the same result are the expressions in options B and C:

`\begin{gathered} B.A(1.04)^(-t) \\ \\ C.A(1.96)^t \end{gathered}`

Therefore, the two expressions that are equivalent are:

`\begin{gathered} B.A(1.04)^(-t) \\ \\ C.A(1.96)^t \end{gathered}`

ANSWER:

`\begin{gathered} \text{ B. A(1.04})^(-t) \\ \\ \text{ C. A(1.96)}^t \end{gathered}`