I’m calculating a discrete integral from distinct water-flow measurements. That means I have a few thousand data values in liter/second and I calculate from them the totally flown water in liter. The accuracy of the data is +/- 0.5 liter and I get one value every 5 seconds. The total time of...
Your function must be monotone increasing and concave for all x. So an exponential function comes into mind. As you have two constraints, try g(x) = a exp( bx). Solving this for your two x values will lead to a very simple result with indeed g(6) = 27.
Erich