Write a recursive rule for the exponential function y = 25(0.2)^x

Question

Write a recursive rule for the exponential function y=25(0.2)^x

Answer 1

f(x + 1) = 0.2f(x)

 

where    f(1) = 25

 

 

f(1) indicates the first value in the growth

f(x) is the previous term

f(x + 1) is the new term

Answer 2

You have to guarantee that x is a positive integer.

 

Integral exponents can be calculated recursively like this:

 

  f(N) =   {           25      if N=0,

 

                       0.2 * f(N-1)

           }

 

In general, it is

 

  f(N) = {   k if N=0,

 

                 base * f(N-1)

           }

 

IN this problem, base = 0.2 and k=25