Model the data using an exponential function $$f ( x ) = A b ^ { x }$$ . $$\begin{array} { | l | l | l | l | }
\hline \boldsymbol { x } & 0 & 1 & 2 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & 350 & 175 & 87.5 \
\hline
\end{array}$$ Select the correct answer.

A) $f ( x ) = 0.5 ( 0.5 ) ^ { x }$
B) $f ( x ) = 350 ( 350 ) ^ { x }$
C) $f ( x ) = 350 ( 0.5 ) ^ { x }$
D) $f ( x ) = 350 ( 0.5 ) ^ { - x }$
E) $f ( x ) = 0.5 ( 350 ) ^ { - x }$

Question

Model the data using an exponential function $$f ( x ) = A b ^ { x }$$ . $$\begin{array} { | l | l | l | l | } 
\hline \boldsymbol { x } & 0 & 1 & 2 \
\hline \boldsymbol { f } ( \boldsymbol { x } ) & 350 & 175 & 87.5 \
\hline
\end{array}$$   Select the correct answer.
 
A) $f ( x ) = 0.5 ( 0.5 ) ^ { x }$
B) $f ( x ) = 350 ( 350 ) ^ { x }$
C) $f ( x ) = 350 ( 0.5 ) ^ { x }$
D) $f ( x ) = 350 ( 0.5 ) ^ { - x }$
E) $f ( x ) = 0.5 ( 350 ) ^ { - x }$

Quizplus · Accepted Answer

The exponential function that models the data is $f(x) = 350(0.5)^x$. This is because when $x=0$, $f(x)=350$, and for each increase in $x$ by 1, $f(x)$ is halved, which matches the behavior of multiplying by $0.5$.

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

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