Chapter 4 - 4.1 Introduction to the Family of Exponential Functions - Exercises and Problems for Section 4.1 - Exercises and Problems - Page 147: 49

\begin{equation} \begin{aligned} y&= 5(4^{-1/6})^{t}\\ &=a4^{kt} \\ a&= 5\\ k&= {-1/6}\\ \end{aligned} \end{equation}

Given $$y = 5(0.5)^{t/3} $$ Rearrange the function to get: \begin{equation} \begin{aligned} y&= 5(0.5)^{t/3}\\ &= 5(0.5^{1/3})^{t}\\ &= 5(1/2^{1/3})^{t}\\ &= 5(1/2^{2/6})^{t}\\ &= 5(1/4^{1/6})^{t}\\ &= 5(4^{-1/6})^{t}\\ y&=a4^{kt} \\ a&= 5\\ k&= {-1/6}\\ \end{aligned} \end{equation}