Does the table represent an exponential function?
x: 1 | 2 | 3 | 4 |
y: 4 | 16 | 64 | 256 |
a. yes
b. no***
it is exponential: y = 4^x
Well, the table does have a pattern of increasing values, but not exactly the kind that we associate with an exponential function. In an exponential function, the values typically increase or decrease by a consistent factor each time. In this case, the values seem to be increasing by powers of 4, which is more indicative of an exponential relationship. So, I would say the answer is... b. no, unless the table is secretly plotting the growth rate of laughter at a clown convention.
To determine whether the table represents an exponential function, we need to check if there is a common ratio between the y-values as the x-values increase. Let's look at the differences between consecutive y-values:
Difference between 16 and 4: 16 - 4 = 12
Difference between 64 and 16: 64 - 16 = 48
Difference between 256 and 64: 256 - 64 = 192
Since the differences are not consistent, we can conclude that the table does not represent an exponential function. Therefore, the correct answer is b. no.
To determine whether the table represents an exponential function, we need to examine the relationship between the x-values and the corresponding y-values.
In an exponential function, the y-values typically increase or decrease at a constant ratio as the x-values change. We can check if the ratios between the y-values are consistent.
In this case, we can see that as x increases by a factor of 1 (from 1 to 2, 2 to 3, and 3 to 4), the y-values increase by a factor of 4 (from 4 to 16, 16 to 64, and 64 to 256). This consistent multiplication by 4 indicates that the table represents an exponential function.
Therefore, the correct answer is "a. yes."