If you have the data for the number of publications in 2017, for instance, and you have also the number of publications (in any field or for any country) in 2015 and you would like to measure the growth rate from 2015 to 2017, then you reduce the number of publications of 2017 from that of 2015, and you you divide the result by the number of publications of 2015 and then multiply by 100. The result is in percents.
First you need to compute the corresponding growth for each year, then compute the total sum of the figures of corresponding growth for each year and then divide it by the number of years, that will give you average annual corresponding growth.