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指数関数 y=2^x について，x が以下の値をとるときの y の値を求めよ。
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
&\colMM{orange}{マイナス乗は}\\
y &= 2^{-2}\\
& \colMM{orange}{\Darr 逆数に}\\
&= \dfrac{1}{2^2} = \dfrac{1}{4} = 0.25
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
&\colMM{orange}{マイナス乗は}\\
y &= 2^{-1.5}\\
& \colMM{orange}{\Darr 逆数に}\\
&= \dfrac{1}{2^{1.5}}\\
& \colMM{green}{\Darr 小数は分数に}\\
&= \dfrac{1}{2^{\frac32}}\\
& \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\
&= \dfrac{1}{\sqrt[2]{2^3}}\\
\\
&= \dfrac{1}{2\sqrt{2}} = \dfrac{\sqrt{2}}{4} \fallingdotseq \dfrac{1.4}{4} = 0.35
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
&\colMM{orange}{マイナス乗は}\\
y &= 2^{-1}\\
& \colMM{orange}{\Darr 逆数に}\\
&= \dfrac{1}{2^1} = \dfrac{1}{2} = 0.5
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
&\colMM{orange}{マイナス乗は}\\
y &= 2^{-0.5}\\
& \colMM{orange}{\Darr 逆数に}\\
&= \dfrac{1}{2^{0.5}}\\
& \colMM{green}{\Darr 小数は分数に}\\
&= \dfrac{1}{2^{\frac12}}\\
& \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\
&= \dfrac{1}{\sqrt[2]{2^1}}\\
\\
&= \dfrac{1}{\sqrt{2}} = \dfrac{\sqrt{2}}{2} \fallingdotseq \dfrac{1.4}{2} = 0.7
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
&\colMM{orange}{０乗は}\\
y &= 2^{0}\\
&= \colBX{bisque}{$1$}
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
y &= 2^{0.5}\\
& \colMM{green}{\Darr 小数は分数に}\\
&= 2^{\frac12}\\
& \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\
&= \sqrt[2]{2^1}\\
\\
&= \sqrt{2} \fallingdotseq 1.4
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
y &= 2^{1} = 2\\
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
y &= 2^{1.5}\\
& \colMM{green}{\Darr 小数は分数に}\\
&= 2^{\frac32}\\
& \colMM{green}{\Darr 分数乗は\sqrt{ルート}に}\\
&= \sqrt[2]{2^3}\\
\\
&= 2\sqrt{2} \fallingdotseq 2 \times 1.4 = 2.8
\end{align*}
【解答】
\newcommand\colUL[2]{\textcolor{#1}{\underline{\color{black}#2}}}
\newcommand\colMM[2]{\textcolor{#1}{\scriptsize\bf\bm #2}}
\newcommand\colBX[2]{\colorbox{#1}{#2}}
\begin{align*}
y &= 2^{2} = 4\\
\end{align*}
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