Functions Modeling Change: A Preparation for Calculus, 5th Edition

Use the fact that $e^{\ln b}=b$ for all positive $b$ to convert the equation into $$y=a(e^{\ln b})^t$$ Next, use the identity that $(a^b)^n=a^{bn}$ to simplify the equation to $$y=ae^{t \ln b}$$ This means that $k$ must be equal to $\ln b$ in the form $y=ae^{kt}$. This makes the statement true.