Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a.
-$\begin{array}{cl}
\hline \mathrm{x} & \mathrm{H}(\mathrm{x}) \
\hline-1 & \frac{5}{8} \
0 & 1 \
1 & \frac{8}{5} \\
2 & \frac{64}{25} \\
3 & \frac{512}{125} \\
\hline
\end{array}$

A) Exponential; $a = \frac { 5 } { 8 }$
B) Exponential; $a = 8$
C) Exponential; $a = \frac { 8 } { 5 }$
D) Not exponential

Question

Determine whether the given function is exponential or not. If it is exponential, identify the value of the base a.
-$\begin{array}{cl}
\hline \mathrm{x} & \mathrm{H}(\mathrm{x}) \
\hline-1 & \frac{5}{8} \
0 & 1 \
1 & \frac{8}{5} \\
2 & \frac{64}{25} \\
3 & \frac{512}{125} \\
\hline
\end{array}$

A) Exponential; $a = \frac { 5 } { 8 }$
B) Exponential; $a = 8$
C) Exponential; $a = \frac { 8 } { 5 }$
D) Not exponential

Quizplus · Accepted Answer

To determine if the function is exponential, we look for a consistent ratio between successive values of $H(x)$. From $H(-1) = \frac{5}{8}$ to $H(0) = 1$, the ratio is $\frac{1}{\frac{5}{8}} = \frac{8}{5}$. From $H(0) = 1$ to $H(1) = \frac{8}{5}$, the ratio is $\frac{8}{5}$. This pattern continues for all given values, indicating the function is exponential with a base of $\frac{8}{5}$.

Determine Whether the Given Function Is Exponential or Not A) Exponential;