Look at this table:
x y
1 5.4
2 10.8
3 21.6
4 43.2
5 86.4
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
This table shows a pattern of each y value being doubled from the previous value. Therefore, it appears to follow an exponential function.
To find the exponential function that models the data, we need to determine the values of a and b.
The initial value (when x = 1) is y = 5.4. Therefore, a = 5.4.
The common ratio (ratio between consecutive y values) is 2. Therefore, b = 2.
Therefore, the exponential function that models the data is:
y = 5.4(2)^x