Find the exponential function that models the data in the table below. $\begin{array}{l|l}
x & f(x) \
\hline-2 & 9 \
-1 & 13.5 \
0 & 20.25 \
1 & 30.375 \
2 & 45.5625
\end{array}$
A) $f ( x ) = 9 \cdot 0.5 ^ { x }$
B) $f ( x ) = 13.5 \cdot 1.5 ^ { x }$
C) $f ( x ) = 20.25 \cdot 1.5 ^ { x }$
D) $f ( x ) = 20.25 \cdot 1.33 ^ { x }$

Question

Quizplus · Accepted Answer

The exponential function that models the data is $f(x) = 20.25 \cdot 1.5^x$. This is evident because the base value when $x = 0$ is $20.25$, and each step in $x$ multiplies the previous value by $1.5$, consistent with the pattern in the table.

Find the Exponential Function That Models the Data in the Table