Determine whether the following table represents and exponential function. Explain why or why not.
x= 0,1.2.3
y=12,16,32,44
A. No, all of the x-values have a constant ratio, but all of the y-values do not have a constant difference.
B. Yes, all of the x-values have a constant ratio, and all of the y-values have a constant difference.
C. Yes, all of the x-values have a constant difference, and all of the y-values have a constant ratio.
D. No, all of the x-values have a constant difference, but all of the y-values do not have a constant ratio.
The correct answer is D. No, all of the x-values have a constant difference, but all of the y-values do not have a constant ratio.
In an exponential function, the x-values would have a constant ratio as they increase or decrease, while the y-values would have a constant ratio as they increase or decrease. In this table, the x-values have a constant difference (0.1) as they increase by 0.1 each time, but the y-values do not have a constant ratio as they increase by 4, then by 16, then by 12. Therefore, this table does not represent an exponential function.