Answer
$1$; $p(t)$ satisfies the given condition.
Work Step by Step
Consider the integral
$I=\int_{0}^{\infty} (\dfrac{1}{50}) e^{-t/50} \ dx \\=(\dfrac{1}{50}) \lim\limits_{a \to \infty} \int_0^a e^{-t/50} \ dx \\=-1 \lim\limits_{a \to \infty} (\dfrac{1}{e^{a/50}}-1)
\\=(-1)(-1)\\=1$
This implies that $p(t)$ satisfies the given condition.
