Which type of function is represented by the table of values below?
x
y
1
4
2
16
3
64
4
256
5
1,024
looks something like
y = 2^x
but you will have to adjust it a bit.
linear
To determine the type of function represented by the table of values, we can look for any patterns or trends in the data.
By examining the values of y for each corresponding value of x, we can see that as x increases, the values of y are increasing exponentially. The values of y are also increasing at a consistent rate.
Based on these observations, the type of function represented by the table of values is an exponential function.
To determine the type of function represented by the table of values, we need to look for a pattern or relationship between the x-values and the y-values.
Let's examine the relationship between x and y. Notice that as x increases, y increases as well, but not at a constant rate. The y-values are increasing exponentially, which means that each y-value is the result of multiplying the previous y-value by a fixed number.
To find this fixed number, we can look at the ratio between successive y-values. Let's calculate the ratios:
4 / 1 = 4
16 / 4 = 4
64 / 16 = 4
256 / 64 = 4
1,024 / 256 = 4
We can see that the ratio between successive y-values is always 4. This tells us that the relationship between x and y follows an exponential function with a base of 4.
Therefore, the type of function represented by the table of values is an exponential function with a base of 4.