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 table values are very close approximations to the function $f(x) = e^{-3x}$. Specifically, note that $f(0) \approx 1$ and $f(1) \approx 0.05$, which corresponds to a decrease of about a factor of $20$ in $f(x)$ as $x$ increments by $1$. This behavior matches the exponential function $e^{-3x}$, so we choose $\boxed{	ext{(B)}\ f(x) = e^{-3x}}$ as our answer.

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