Find the exponential function that models the data in the table below. $\begin{array}{l|r}
\mathrm{x} & \mathrm{f}(\mathrm{x}) \
\hline-2 & 22 \
-1 & 15.4 \
0 & 10.78 \
1 & 7.546 \
2 & 5.2822
\end{array}$

A) $f ( x ) = 10.78 \cdot 1.3 ^ { x }$
B) $f ( x ) = 22 \cdot 0.7 ^ { x }$
C) $f ( x ) = 15.4 \cdot 1.7 ^ { x }$
D) $f ( x ) = 10.78 \cdot 0.7 ^ { x }$

Question

Find the exponential function that models the data in the table below. $\begin{array}{l|r}
\mathrm{x} & \mathrm{f}(\mathrm{x}) \
\hline-2 & 22 \
-1 & 15.4 \
0 & 10.78 \
1 & 7.546 \
2 & 5.2822
\end{array}$

A) $f ( x ) = 10.78 \cdot 1.3 ^ { x }$
B) $f ( x ) = 22 \cdot 0.7 ^ { x }$
C) $f ( x ) = 15.4 \cdot 1.7 ^ { x }$
D) $f ( x ) = 10.78 \cdot 0.7 ^ { x }$

Quizplus · Accepted Answer

The function $f(x) = 10.78 \cdot 0.7^x$ correctly models the data because it starts with a base value of 10.78 when $x = 0$, and each step in $x$ results in the value being multiplied by 0.7, which matches the pattern observed in the table.

Find the Exponential Function That Models the Data in the Table