Look at this table:
x y
–
5
–
6.6
–
4
–
3.5
–
3
–
0.4
–
2 2.7
–
1 5.8
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the data can be modeled by a linear or exponential function, we can look for a pattern in the values of y as x increases or decreases.
Looking at the table:
x y
–5
–6.6
–4
–3.5
–3
–0.4
–2 2.7
–1 5.8
As x increases, y does not increase or decrease at a constant rate, which indicates that the data is not linear. Additionally, the y values do not appear to be increasing or decreasing by a consistent multiplicative factor, indicating that the data is not exponential either.
Since the data does not follow a clear pattern for either a linear or exponential function, it is not possible to write a linear function (y=mx+b) or an exponential function (y=a(b)x) to precisely model the data.