The function is in fact a polynomial and the degree of the polynomial is 7.
I think it is c, I could be wrong though

Let's substitute the value of x as 8 in the given equation to find the value of y ~
Year rank population
1790 3 18320
1800 4 24937
1810 4 33787
1820 4 43298
1830 4 61392
1840 5 93383
1850 3 136881
1860 5 177840
1870 7 250526
1880 5 362839
1890 6 448477
1900 5 560892
1910 5 670585
1920 7 748060
1930 9 781188
1940 9 770816
1950 10 801444
1960 13 697197
1970 16 641071
1980 20 562994
1990 20 574283