Alright so first of all thanks to anyone who helps me out, ive been stuck on this problem for days and its really irritating. So i have a bunch of points, and im supposed to graph them and then find a function that models it really well algebraically. So basically find an equation that fits the data nicely.

Here are the points:

x: 1932 1936 1948 1952 1956 1960 1964 1968 1972 1976 1980

y: 197 203 198 204 212 216 218 224 223 225 236

And heres the graph:

Heres a closeup:

So basically, the base function i though that fits it best is f(x)= x^(1/2), and through trial and error the best curve i came up with is f(x)+59*x^(1/2)-2396.5.

So i dont know, i dont get how i can find an equation algebraically, i know that the base formula is f(x)=a(b(x-h)^(1/2))+k, but if i try solving that i came up with a negative square root, or both the variables cancel. So i honestly dont know what to do. Is the base function appropriate? Should i try something else? If not, how do i find the equation by hand?

Thanks so much to anyone whos willing to take the time and help me