Make an InterpolatingFunction object that will go through the given points:

points = {{0,0},{10.,227.04},{15.,362.78},{20.,517.35},{22.5,602.97},{30.,901.67}};

Only the domain is shown in standard output format:

ifun = Interpolation[points]

Evaluate the function at a point in the domain:

ifun[22.5]

Plot the function over its domain, showing the interpolation points:

Plot[ifun[x], {x,0,30}, Epilog->Map[Point, points]]