Sorry to shock you, but not every piece of text on the internet holds water mathematically.
Plot a cubic polynomial in time, at^3 + bt^2 + c*t + d. Use Excel. The curve either diverges to + or - infinity at each end, or it's a constant. That's not the behavior of the dashed red curve in the OP.
What it could be is some kind of cubic spline. But it is not a cubic polynomial in time.
A cubic polynomial goes to +infinity on one side and -infinity on the other. So taking exp, log, etc won't make it go to 0 on both sides. I can think of two possible explanations: 1) the leading coefficient happens to be 0, so it's actually quadratic fit 2) the leading coefficient is nonzero, so somewhere to the left or right the graph starts rising again, but it's not visible due to cropping. Anyway by now we've spent more time thinking about this than any of the participants, so we should call it a day.
Plot a cubic polynomial in time, at^3 + bt^2 + c*t + d. Use Excel. The curve either diverges to + or - infinity at each end, or it's a constant. That's not the behavior of the dashed red curve in the OP.
What it could be is some kind of cubic spline. But it is not a cubic polynomial in time.