Exponential graph question (1 Viewer)

kpad5991 · Jan 18, 2017

Explain why y = (0.5)^x is not a raising exponential curve by showing that y = (0.5)^x is the same as 2^-x

1729 · Jan 18, 2017

kpad5991 said:
Explain why y = (0.5)^x is not a raising exponential curve by showing that y = (0.5)^x is the same as 2^-x

$$\noindent $(0.5)^{x} = \left (\frac{1}{2}\right)^{x} = (2^{-1})^{x} = 2^{-x}$, as required. \\\\Now, we have $y = 2^{-x}$. This is not a rising curve as it is simply the reflection of the curve $y = 2^{x}$ about the $y$-axis. \\\\This result can also be obtained as follows: let $y = f(x).$ \\Now, $f'(x) = -2^{-x}$ln$2$. We can therefore conclude that $f'(x) < 0$ for all $x \in D_{f}$\\\\ Graphically, this result means that the curve is monotonic decreasing, that is, not a rising curve.$

Exponential graph question (1 Viewer)

kpad5991

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