Answer
$101\text{ countries}$
Work Step by Step
We use a graphing calculator to plot the points $(x,y)$ from the given data and the best-fitting line (see graph).
The equation of the best-fitting line provided by the graphing calculator is:
$$y=1.7683x+40.7245.\tag1$$
The corresponding value of $x$ for $2014$ is $$x=2014-1980=34.$$
Use Eq. $(1)$ to calculate the number of participating countries $y$ in $2014$.
$$y=1.7683(34)+40.7245\approx 101.$$
So the number of participating countries in $2014$ is approximately $101$.
