Answer
$1998$
Work Step by Step
We are given the function:
$$Sf(t)=-0.0076t^4+0.14t^3-0.62t^2+0.52t+5.5,$$
where $t\geq 0$.
We graph the function $S$ and the line $y=8$, then find their first intersection:
$$(6.729,8)$$
It follows that the first year when the number of participants was greater than $8$ million was $1992+6=1998$.