Answer
Any year after (and including) 2041
Work Step by Step
$c = -9.4t +431$
c = # cigarettes
t = # years after 2000
at most 50 billion cigarettes
$50 \geq -9.4t + 431$
$50+9.4t-50 \geq -9.4t + 431+9.4t-50$
$9.4t \geq 381$
$9.4t/9.4 \geq 381/9.4$
$t \geq 40.53$
We want the next year, so $t = 41$