Determine $f ( x )$ from the table.
The values from the table are given to the nearest ten thousandth. Select the correct answer.
$\begin{array}{|r|c|}
\hline x & f(x) \
\hline-1 & 20.0855 \
\hline 0 & 1 \
\hline 1 & 0.0498 \
\hline 2 & 0.0025 \
\hline
\end{array}$

A) $f ( x ) = e ^ { 3 x }$
B) $f ( x ) = e ^ { - 3 x }$
C) $f ( x ) = 3 x ^ { - 3 }$
D) $f ( x ) = x e ^ { - 3 }$
E) $f ( x ) = x ^ { - 3 }$

Question

Determine $f ( x )$ from the table.
The values from the table are given to the nearest ten thousandth. Select the correct answer.
$\begin{array}{|r|c|}
\hline x & f(x) \
\hline-1 & 20.0855 \
\hline 0 & 1 \
\hline 1 & 0.0498 \
\hline 2 & 0.0025 \
\hline
\end{array}$

A) $f ( x ) = e ^ { 3 x }$
B) $f ( x ) = e ^ { - 3 x }$
C) $f ( x ) = 3 x ^ { - 3 }$
D) $f ( x ) = x e ^ { - 3 }$
E) $f ( x ) = x ^ { - 3 }$

Quizplus · Accepted Answer

The given values are very close to the function $f(x)=e^{-3x}$ evaluated at their respective x-values. For example, $f(-1)=e^{-3(-1)}=e^3=20.0855$ (rounded to the nearest ten-thousandth). Similarly, $f(0)=e^{-3(0)}=1$, $f(1)=e^{-3(1)}=0.0498$, and $f(2)=e^{-3(2)}=0.00247875$. No other choices match the table as closely as $f(x)=e^{-3x}$.

Determine f(x)f ( x )f(x) From the Table xf(x)−120.08550110.049820.0025\begin{array}{|r|c|}\hline x & f(x) \\\hline-1 & 20.0855 \\\hline 0 & 1 \\\hline 1 & 0.0498 \\\hline 2 & 0.0025 \\\hline\end{array}x−1012​f(x)20.085510.04980.0025​​

Determine $f ( x )$ From the Table $\begin{array}{|r|c|}\hline x & f(x) \\\hline-1 & 20.0855 \\\hline 0 & 1 \\\hline 1 & 0.0498 \\\hline 2 & 0.0025 \\\hline\end{array}$