Answer
(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 $~~x \gt 23.026$
