In this paper, methods introduced earlier by the author [1] are used to obtain simple, accurate formulas for the decision boundaries for sequential probability ratio tests for simple hypotheses and alternatives on the mean $\theta$ of the exponential distribution $\theta^{-1} \exp(-u/\theta)$. Examples are provided to indicate the accuracy and the degree of complexity of the results. It is hoped that the results given here will find applications in life testing and statistical studies of radioactive decay.