Answer
$2005$.
About $3.36$ million barrels/day
Work Step by Step
The graph of P(t) is a parabola that opens down (leading coefficient is negaative.)
$a=-0.022, b=0.2, c=2.9$
The vertex is the point of maximum, and has coordinates
$t=-\displaystyle \frac{b}{2a}$ and $P(-\displaystyle \frac{b}{2a})$
$t=-\displaystyle \frac{0.2}{-2\times 0.022}\approx 4.545$, which corresponds to year $2005$.
$P(4.545)\approx 3.36$ million barrels/day
