Chapter 2 - Section 2.6 - Limits at Infinity; Horizontal Asymptotes - 2.6 Exercises - Page 140: 70

(a) On the graph , we can see that $~~e^{-x/10} \lt 0.1~~$ when $~~x \gt 23.1$ (b) $x = 23.026$

Work Step by Step

(a) We can graph the function $f(x) = e^{-x/10}$ and the function $y = 0.1$ On the graph , we can see that $~~e^{-x/10} \lt 0.1~~$ when $~~x \gt 23.1$ (b) We can find the exact value of $x$ as follows: $e^{-x/10} = 0.1$ $-x/10 = ln(0.1)$ $x = -10~ln(0.1)$ $x = 23.026$ $e^{-x/10} \lt 0.1~~$ when $~~x \gt 23.026$

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