Find the exponential function that models the data in the table below. $\begin{array}{l|l}
x & f(x) \
\hline-2 & -45 \
-1 & -27 \
0 & -16.2 \
1 & -9.72 \
2 & -5.832
\end{array}$

A) $f ( x ) = - 45 \cdot 0.6 ^ { x }$
B) $f ( x ) = - 16.2 \cdot 0.6 ^ { x }$
C) $f ( x ) = 16.2 \cdot 1.4 ^ { x }$
D) $f ( x ) = - 27 \cdot 1.6 ^ { x }$

Question

Find the exponential function that models the data in the table below. $\begin{array}{l|l}
x & f(x) \
\hline-2 & -45 \
-1 & -27 \
0 & -16.2 \
1 & -9.72 \
2 & -5.832
\end{array}$

A) $f ( x ) = - 45 \cdot 0.6 ^ { x }$
B) $f ( x ) = - 16.2 \cdot 0.6 ^ { x }$
C) $f ( x ) = 16.2 \cdot 1.4 ^ { x }$
D) $f ( x ) = - 27 \cdot 1.6 ^ { x }$

Quizplus · Accepted Answer

The base of the exponential function can be found by observing how the function value changes as $x$ increases by 1. From $f(-1) = -27$ to $f(0) = -16.2$, the function value is multiplied by $0.6$ ($-27 \times 0.6 = -16.2$). This pattern continues for other values of $x$, confirming the base of the exponential function is $0.6$. The initial value $f(0) = -16.2$ indicates the coefficient in front of the base, leading to the function $f(x) = -16.2 \cdot 0.6^x$.

Find the Exponential Function That Models the Data in the Table