Chapter 4 - 4.1 Introduction to the Family of Exponential Functions - Exercises and Problems for Section 4.1 - Exercises and Problems - Page 147: 48

\begin{equation} \begin{aligned} y&= 5(0.5^{1/3})^{t}\\ &=ab^t \\ a&= 5\\ b&= 0.5^{1/3}\\ \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}\\ y&=ab^t \\ a&= 5\\ b&= 0.5^{1/3}\\ \end{aligned} \end{equation}