Chapter 4 - Exponential Functions - 4.5 The Number e - Exercises and Problems for Section 4.5 - Exercises and Problems - Page 176: 56

$\lim _{t \rightarrow-\infty} 2 e^{-0.1 t+6}=\infty$

The function $ e^{-0.1 t}$, approaches infinity as $t$ takes on larger negative numbers. Therefore: $$ \lim _{t \rightarrow-\infty} 2 e^{-0.1 t+6}=\lim _{t \rightarrow-\infty} (2e^{6}\cdot e^{-0.1 t}) =\infty $$