Answer
Exponential function
Work Step by Step
First calculate slope of two consecutive ordered pair coordinates:
The coordinates are \[\left( 0,1 \right),\left( 1,5 \right),\left( 2,25 \right),\left( 3,125 \right),\text{ and}\left( 4,625 \right)\].
\[\text{Since, }m=\left( \frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \right)\],
Now, calculate slopes of two consecutive ordered pair of coordinates:
\[\begin{align}
& {{m}_{1}}=\left( \frac{5-1}{1-0} \right)=\frac{4}{1}=4 \\
& {{m}_{2}}=\left( \frac{25-5}{2-1} \right)=\frac{20}{1}=20 \\
& {{m}_{3}}=\left( \frac{125-25}{3-2} \right)=\frac{100}{1}=100 \\
& {{m}_{4}}=\left( \frac{625-125}{4-3} \right)=\frac{500}{1}=500
\end{align}\]
It can be seen that, slopes of any two consecutive coordinate pairs are positive, and slope is strictly increasing with high rate, as x increasing. It is the property of exponential function.
Therefore, the ordered pair value of this table represents the graph of an exponential function.
