Look at this table:
x y
–
4
–
18
–
3
–
13
–
2
–
8
–
1
–
3
0 2
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the given data can be modeled using a linear or exponential function, we need to check if there is a constant rate of change or constant ratio between the x and y values.
Looking at the x values, we notice that they are decreasing by 1 each time (from -4 to 0). However, the y values do not have a consistent difference between them. Therefore, it is not a linear function.
Now, let's analyze if it can be modeled as an exponential function.
If we calculate the ratios between successive y values, we have:
-4 / 18 ≈ -0.222
18 / 3 = 6
3 / 13 ≈ 0.231
13 / 2 = 6.5
2 / 8 = 0.25
8 / 1 = 8
1 / 3 ≈ 0.333
3 / 2 = 1.5
2 / 0.5 = 4
These ratios are not constant. Therefore, the given data cannot be represented by an exponential function either.
In conclusion, the given data cannot be modeled using a linear function or an exponential function.