Given that t = \(2 ^{-x}\), find \(2 ^{x + 1}\) in terms of t.
A
\(\frac{2}{t}\)
B
\(\frac{t}{2}\)
C
\(\frac{1}{2t}\)
D
t
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
t = \(2^{-x} = \frac{1}{2^{x}}\)
\(\implies 2^{x} =\frac{1}{t}\)
\(2^{x+1} = 2^{x} \times 2^{1}\)
= \(\frac{1}{t} \times 2 = \frac{2}{t}\)
Source: Myschool Past Questions Archive (Record #50130)