Look at this table:
x y
–
1 1.4
0 4.2
1 12.6
2 37.8
3 113.4
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Based on the given data, we can observe that the values of y are increasing at a much faster rate compared to the values of x. This suggests that an exponential function would be a better fit for the data.
To determine the exponential function, let's first find the common ratio, which is the ratio between consecutive values of y.
When x = 1, y = 1.4
When x = 2, y = 4.2
Ratio = y(2) / y(1) = 4.2 / 1.4 = 3
Since we have found the common ratio, we can write the exponential function in the form y = a(b)^x.
Using the data point (1, 1.4):
1.4 = a(b)^1
Using the common ratio we found:
1.4 = a(3)^1
1.4 = 3a
Solving for a, we get a = 1.4 / 3 = 0.4667 (rounded to 4 decimal places).
Therefore, the exponential function that models the data is:
y = 0.4667(3)^x