Two points define rate of growth but not acceleration but there is that 228 figure and curve looks smooth, so we can try different curves and see if any matches the 228 figure.
I just opened a spreadsheet, it is easy to play about with the numbers:
I tried various steady growth factors. To get from 0.6 to 4.1 seems to require rate to be about 1.01485 times the previous year. This gets to 238 by 2010. Fairly close.
(A steady increase in the rate going from .6 to 4.1 gets a total of 308. So steady growth factor was much nearer than this.)
That is only two types of curve tried. It is quite possible that a different type of curve could do it. Another possibility is the curve might actually be a compound like 1% growth rate for first x years then 1.9% for next y years .....
Wikipedia says things like
This network was used, in combination with satellite altimeter data, to establish that global mean sea-level rose 19.5 cm (7.7 in) between 1870 and 2004 at an average rate of about 1.44 mm/yr (1.7 mm/yr during the 20th century).[30] This is an important confirmation of climate change simulations which predicted that sea level rise would accelerate in response to global warming. In Australia, data collected by the Commonwealth Scientific and Industrial Research Organisation (CSIRO) show the current global mean sea level trend to be 3.2 mm (0.13 in) per year, a doubling of the rate during the 20th century.[31][32]
Not too difficult to play around with a spreadsheet to try things out.
Suspect you could get quite different answers by 2100 by assuming different curves. Not quite enough info for me to tie it down. Could try measuring height of line at various points to try to help constrain it but the line looks quite thick and I am therefore not to sure if this will help or if measurement error in this will mean it won't help.
Spreadsheet is probably easier than calculus. Either way need to know details of the curve.