Look at this table:
x y
–
1 0.28
0 0.84
1 2.52
2 7.56
3 22.68
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
First, let's observe the relationship between x and y. By examining the data, we can see that as x increases, y also increases, but not at a constant rate. This suggests that the relationship between x and y is most likely exponential.
To determine the exponential function that models the data, we need to find the values of a and b.
Using the given data, we can see that when x = 0, y = 0.84. This gives us the value of a:
0.84 = a(b)^0
0.84 = a
Next, we can choose any other set of x and y values from the table to find the value of b. Let's use the values when x = 1 and y = 2.52:
2.52 = 0.84(b)^1
2.52 = 0.84b
b = 2.52/0.84
b ≈ 3
Therefore, the exponential function that models the data is:
y = 0.84(3)^x