Model the data using an exponential function $$f ( x ) = A b ^ { x }$$ . $$\begin{array} { | l | l | l | }
\hline \boldsymbol { x } & 1 & 2 \
\hline f ( x ) & 13 & 16.9 \
\hline
\end{array}$$ Select the correct answer.

A) $f ( x ) = 10 ( 10 ) ^ { x }$
B) $f ( x ) = 1.3 ( 1.3 ) ^ { - x }$
C) $f ( x ) = 10 ( 1.3 ) ^ { x }$
D) $f ( x ) = 10 ( 1.3 ) ^ { - x }$
E) $f ( x ) = 1.3 ( 10 ) ^ { x }$

Question

Model the data using an exponential function $$f ( x ) = A b ^ { x }$$ . $$\begin{array} { | l | l | l | } 
\hline \boldsymbol { x } & 1 & 2 \
\hline f ( x ) & 13 & 16.9 \
\hline
\end{array}$$   Select the correct answer.
 
A) $f ( x ) = 10 ( 10 ) ^ { x }$
B) $f ( x ) = 1.3 ( 1.3 ) ^ { - x }$
C) $f ( x ) = 10 ( 1.3 ) ^ { x }$
D) $f ( x ) = 10 ( 1.3 ) ^ { - x }$
E) $f ( x ) = 1.3 ( 10 ) ^ { x }$

Quizplus · Accepted Answer

To find the correct model, we use the given data points (1, 13) and (2, 16.9) in the exponential function $f(x) = Ab^x$. For $x = 1$, $f(1) = 13 = Ab^1 = Ab$. For $x = 2$, $f(2) = 16.9 = Ab^2$.Dividing the second equation by the first gives $\frac{16.9}{13} = b$, which simplifies to $b = 1.3$.Substituting $b = 1.3$ into $f(1) = 13 = A(1.3)^1$ gives $A = 10$.Therefore, the correct model is $f(x) = 10(1.3)^x$.

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

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