x y
0 2
1 4
2 8
3 16
4 32
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
This data can be modeled by an exponential function.
To determine the values of a and b in the equation y = a(b)^x, we can substitute any two points from the given data.
Using the points (0, 2) and (1, 4):
2 = a(b)^0
4 = a(b)^1
Since any number raised to the power of 0 is 1, equation 1 becomes:
2 = a(1)
Therefore, we can determine that a = 2.
Substituting this value into the second equation:
4 = 2(b)^1
Therefore, b = 2.
Hence, the exponential function that models the data is:
y = 2(2)^x