1. **State the problem:** Find the limit $ \lim_{x \to -\infty} 4(5^x) + 2 $. 2. **Recall the behavior of exponential functions:** For any base $ a > 1 $, $ a^x \to 0 $ as $ x \to -\infty $. 3. **Apply this to $ 5^x $:** Since 5 is greater than 1, $ 5^x \to 0 $ as $ x \to -\infty $. 4. **Evaluate the limit:** $$\lim_{x \to -\infty} 4(5^x) + 2 = 4 \cdot 0 + 2 = 2$$ **Final answer:** $ 2 $