Look at this table:
x y
1
–
3
2
–
9
3
–
27
4
–
81
5
–
243
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
This table represents an exponential function because each value of y is obtained by multiplying the previous value by a constant factor of 3.
To find the function, we can look at the pattern:
- The value of y starts at 1 and increases by a factor of 3 each time (1, 3, 9, 27, 81, 243).
- The value of x increases by 1 each time (1, 2, 3, 4, 5).
We can represent this pattern in the form y = a(b)^x:
y = 1(3)^x