To check if the given line is exponential, we can starting by making a table for a set of values. Let's do like in the picture, for x = 0, x = 1, x = 2:
[tex]\begin{gathered} (5\cdot0)^3=0^3=0 \\ (5\cdot1)^3=5^3=125 \\ (5\cdot2)^3=10^3=1000 \end{gathered}[/tex]
Here is the table then:
x | y
0 | 0
1 | 125
2 | 1000
For an exponential line, we can divide two y values of consecutive x values, and all consecutive values mus t be equal.
We would start by doing:
[tex]\frac{125}{0}[/tex]
And comparing it to
[tex]\frac{1000}{125}[/tex]
To see if they are equal. However, we can't divide by zero. Because of this, (5x)³ can't be exponential.
To be a linear line or straight line, the difference between consecutive values must be equal, so we should compare:
[tex]125-0=125[/tex]
With:
[tex]1000-125=875[/tex]
Because they are not equal, (5x)³ is not linear nor straight.
So it can't be alternatives A, B or C. So It has to be alternative D.
