Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. $\begin{array}{r|rrrr}
\mathrm{x} & 1 & 2 & 3 & 4 \
\hline \mathrm{y} & 580 & 620 & 670 & 750
\end{array}$

A) $f ( x ) = ( 1.09 ) ( 527.34 ) ^ { x }$
B) $f ( x ) = ( 567.57 ) ( 0.17 ) ^ { x }$
C) $f ( x ) = ( 527.34 ) ( 1.09 ) ^ { x }$
D) $f ( x ) = ( 0.17 ) ( 567.57 ) ^ { x }$

Question

Find the exponential function f that models this data. Round the coefficients to the nearest hundredth. $\begin{array}{r|rrrr}
\mathrm{x} & 1 & 2 & 3 & 4 \
\hline \mathrm{y} & 580 & 620 & 670 & 750
\end{array}$

A) $f ( x ) = ( 1.09 ) ( 527.34 ) ^ { x }$
B) $f ( x ) = ( 567.57 ) ( 0.17 ) ^ { x }$
C) $f ( x ) = ( 527.34 ) ( 1.09 ) ^ { x }$
D) $f ( x ) = ( 0.17 ) ( 567.57 ) ^ { x }$

Quizplus · Accepted Answer

The exponential function that models the given data is of the form $f(x) = ab^x$, where $a$ is the initial value when $x=0$, and $b$ is the growth factor. To find the correct model, we need to look for a pattern in the y-values that fits an exponential growth. The option $f(x) = (527.34)(1.09)^x$ suggests an initial value of 527.34 when $x=0$ and a growth factor of 1.09, which means each step in $x$ increases the value of $f(x)$ by a factor of 1.09. This option is consistent with the pattern of growth observed in the data, where each subsequent value of $y$ is approximately 1.09 times the previous value, after adjusting for the initial offset.

Find the Exponential Function F That Models This Data x1234y580620670750\begin{array}{r|rrrr}\mathrm{x} & 1 & 2 & 3 & 4 \\\hline \mathrm{y} & 580 & 620 & 670 & 750\end{array}xy​1580​2620​3670​4750​​

Find the Exponential Function F That Models This Data $\begin{array}{r|rrrr}\mathrm{x} & 1 & 2 & 3 & 4 \\\hline \mathrm{y} & 580 & 620 & 670 & 750\end{array}$