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WAEC Mathematics 2017 Paper

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Question : 31

Total: 49

Given that t =

2^{-x}

2^{x+1}

in terms of t.

$\frac{2}{t}$
$\frac{t}{2}$
$\frac{1}{2t}$
t

Solution:

Concept:

Use the property

2^{x+1} = 2 \times 2^x

and express

2^x

in terms of

t

.

Explanation:

Given

t = 2^{-x}

.

Since

2^{-x} = \frac{1}{2^x}

, we have

t = \frac{1}{2^x}

.

Taking reciprocals on both sides gives

2^x = \frac{1}{t}

.

Now,

2^{x+1} = 2^x \times 2^1

.

Substitute

2^x = \frac{1}{t}

:

2^{x+1} = \frac{1}{t} \times 2

.

Therefore,

2^{x+1} = \frac{2}{t}

.

Answer:

\frac{2}{t}

, which is option A.

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