Model the data using an exponential function $f ( x ) = A b ^ { x }$ . $$\begin{array} { | l | l | l | l | }
\hline \boldsymbol { x } & 0 & 1 & 2 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & 40 & 80 & 160 \
\hline
\end{array}$$ Select the correct answer.

A) $f ( x ) = 40 ( 2 ) ^ { x }$
B) $f ( x ) = 40 ( 2 ) ^ { - x }$
C) $f ( x ) = 2 ( 40 ) ^ { - x }$
D) $f ( x ) = 2 ( 2 ) ^ { x }$
E) $f ( x ) = 40 ( 40 ) ^ { x }$

Question

Model the data using an exponential function $f ( x ) = A b ^ { x }$ . $$\begin{array} { | l | l | l | l | } 
\hline \boldsymbol { x } & 0 & 1 & 2 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & 40 & 80 & 160 \
\hline
\end{array}$$  Select the correct answer.
 
A) $f ( x ) = 40 ( 2 ) ^ { x }$
B) $f ( x ) = 40 ( 2 ) ^ { - x }$
C) $f ( x ) = 2 ( 40 ) ^ { - x }$
D) $f ( x ) = 2 ( 2 ) ^ { x }$
E) $f ( x ) = 40 ( 40 ) ^ { x }$

Quizplus · Accepted Answer

The exponential function that models the data is $f(x) = 40(2)^x$. This is because when $x=0$, $f(x)=40$, which matches the initial value $A=40$, and the rate of increase is by a factor of 2 for each increment in $x$, indicating $b=2$.

Model the Data Using an Exponential Function f(x)=Abxf ( x ) = A b ^ { x }f(x)=Abx

Model the Data Using an Exponential Function $f ( x ) = A b ^ { x }$