Answer
(a) When $x = 1.0~m$: $~~~E_x = 27~V/m$
(b) When $x = 2.0~m$: $~~~E_x = 3.7~V/m$
Work Step by Step
(a) $V = 100~e^{-2x}~V$
$\frac{dV}{dx} = -200~e^{-2x}~V/m$
We can find $E_x$ when $x = 1.0~m$:
$E_x = -\frac{dV}{dx}$
$E_x = -(-200~e^{-2x})~V/m$
$E_x = 200~e^{(-2)(1.0)}~V/m$
$E_x = 27~V/m$
(b) We can find $E_x$ when $x = 2.0~m$:
$E_x = -\frac{dV}{dx}$
$E_x = -(-200~e^{-2x})~V/m$
$E_x = 200~e^{(-2)(2.0)}~V/m$
$E_x = 3.7~V/m$