beginning - the population is 100

1st year - population from last year grows by 5% that is 100 + 0.05*100 = 100*1.05

2nd year - population from 1st year grows by 5% that is 100*1.05*1.05 = 100*1.05^2

3rd year - population from 2nd year grows by 5% that is 100*1.05*1.05*1.05 = 100*1.05^3

.....

after 50 years the population will be 100*1.05^50 = 1147 rounded to integer

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