Question

In an exponential decay function, the base of the exponent is a value between 0 and 1. Thus, for some number b > 1, the exponential decay function can be written as f(X) = a ∙(1/b)X. Use this formula, along with the fact that b = en, to show that an exponential decay function takes the form f(x) = a(e)−nx for some positive number n. 

Answer 1

The exponential decay function is:

f(x) = a∙(1/b)x

 

Suppose f is the exponential decay function f(x) = a∙(1/b)x such that b > 1.

Then for some number n > 0, then;

f(x) = a∙(1/b)x

      = a(b-1)x

      = a{(en)-1}x

Further solve,

     = a(e-n)x

     = a(e)-nx

 

Hence, the exponential decay function is;

f(x) = a(e)-nx

Hence, the exponential decay function is;

f(x) = a(e)-nx