Find the exponential function that models the data in the table below. Round the coefficients to the nearest hundredth. $\begin{array}{c|c|c|c|c|c}
\mathrm{x} & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{y} & 4.0 & 4.8 & 6.2 & 7.8 & 9.9
\end{array}$

A) $f ( x ) = \frac { 3.95 } { 1 + 510.08 e ^ { - 2 x } }$
B) $f ( x ) = 3.11 ( 1.26 ) ^ { x }$
C) $f ( x ) = \frac { 3.95 } { 1 + 511.07 e ^ { - 2 x } } + 4.45$
D) $f ( x ) = 3.33 ( 1.20 ) ^ { x }$

Question

Find the exponential function that models the data in the table below. Round the coefficients to the nearest hundredth. $\begin{array}{c|c|c|c|c|c}
\mathrm{x} & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{y} & 4.0 & 4.8 & 6.2 & 7.8 & 9.9
\end{array}$

A) $f ( x ) = \frac { 3.95 } { 1 + 510.08 e ^ { - 2 x } }$
B) $f ( x ) = 3.11 ( 1.26 ) ^ { x }$
C) $f ( x ) = \frac { 3.95 } { 1 + 511.07 e ^ { - 2 x } } + 4.45$
D) $f ( x ) = 3.33 ( 1.20 ) ^ { x }$

Quizplus · Accepted Answer

The exponential function that models the data is of the form $f(x) = ab^x$. To find the correct coefficients, we can use two points from the table to form equations and solve for $a$ and $b$. Using $x=1, y=4.0$ and $x=2, y=4.8$, we can set up the equations $4 = ab^1$ and $4.8 = ab^2$. Solving these equations simultaneously would give us values close to $a = 3.11$ and $b = 1.26$, which matches choice B.

Find the Exponential Function That Models the Data in the Table