6.1 Exercise 93

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 $f \left(x\right) = a \cdot \left(\frac{1}{b}\right)^{x} .$ Use this formula, along with the fact that $b = e^{n} ,$ to show that an exponential decay function takes the form $f \left(x\right) = a \left(e\right)^{- n x}$ for some positive number $n$ .