Question

Write a recursive rule for the function.
f(x) = 80(3/4)^x

Answer 1

• f(0) = 80
• f(x) = (3/4)×f(x-1)

Explanation:

The multiplier of 80 is the value of the function when x=0. For a recursive rule, an initial value is needed. Here, that value can be f(0) = 80.

The decay factor of 3/4 tells you that each successive term of the sequence will be 3/4 of the value of the one before. That is, f(x) = (3/4)×f(x -1).

The entire recursive rule consists of a relation between terms and any initial conditions required:

• f(0) = 80
• f(x) = (3/4)×f(x-1)