Answer:
Exponentially.
Explanation:
The given table :
x f(x)
0 3
1 6
2 12
3 24
We can see that the function is increasing (as the x-value increases , the value of y also increases)
Further explanation:
- For linear function, the rate of change of y with respect to x is constant.
In given table , From x = 0 to x = 1 , change in y = 6-3 = 3
From x = 1 to x = 2 , change in y = 12-6 = 6
But 6 ≠ 3
So the rate of change is not constant.
Thus , the given is not representing a linear function.
-
For quadratic function, the second difference(between y-values) is constant.
In given table , From x = 0 to x = 1 , change in y = 6-3 = 3
From x = 1 to x = 2 , change in y= 12-6 = 6
From x = 2 to x = 3 , change in y= 24-12 = 12
Second difference (between y-values): 6-3 = 3
12-6 = 6
But 6 ≠ 3
So the second difference is not constant.
Thus , the given is not representing a quadratic function.
-
For exponential function, the common ratio between consecutive y-values is constant.
In given table , From x=0 to x=1 , [tex]\dfrac{6}{3}=2[/tex]
From x=1 to x=2 , [tex]\dfrac{12}{6}=2[/tex]
From x=2 to x=3 , [tex]\dfrac{24}{12}=2[/tex]
It means , the common ratio is constant.
Therefore, the given function is increasing exponentially.
Learn more : https://brainly.com/question/12548968 [Answered by MrScienceGuy ]
https://brainly.com/question/12878444 [Answered by Lidaralbany]
Keywords : Linear function , Quadratic function , Exponential function.
