Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. $\begin{array}{r|rrrr}
x & 3 & 6 & 9 & 12 \
\hline y & 12.2 & 36.2 & 73.5 & 151
\end{array}$

A) $\mathrm { f } ( \mathrm { x } ) = ( 1.63 ) ( 1.78 ) ^ { \mathrm { x } }$
B) $f ( x ) = ( 1.32 ) ( 5.97 ) ^ { x }$
C) $\mathrm { f } ( \mathrm { x } ) = ( 5.97 ) ( 1.32 ) ^ { \mathrm { x } }$
D) $f ( x ) = ( 1.78 ) ( 1.63 ) ^ { x }$

Question

Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. $\begin{array}{r|rrrr}
x & 3 & 6 & 9 & 12 \
\hline y & 12.2 & 36.2 & 73.5 & 151
\end{array}$

A) $\mathrm { f } ( \mathrm { x } ) = ( 1.63 ) ( 1.78 ) ^ { \mathrm { x } }$
B) $f ( x ) = ( 1.32 ) ( 5.97 ) ^ { x }$
C) $\mathrm { f } ( \mathrm { x } ) = ( 5.97 ) ( 1.32 ) ^ { \mathrm { x } }$
D) $f ( x ) = ( 1.78 ) ( 1.63 ) ^ { x }$

Quizplus · Accepted Answer

The exponential function is of the form $ f(x) = ab^x $. By analyzing the given data, the base $ b $ is approximately 1.32, and the initial value $ a $ is approximately 5.97, which matches option C.

Find the Exponential Function F That Models This Data x36912y12.236.273.5151\begin{array}{r|rrrr}x & 3 & 6 & 9 & 12 \\\hline y & 12.2 & 36.2 & 73.5 & 151\end{array}xy​312.2​636.2​973.5​12151​​

Find the Exponential Function F That Models This Data $\begin{array}{r|rrrr}x & 3 & 6 & 9 & 12 \\\hline y & 12.2 & 36.2 & 73.5 & 151\end{array}$