finding the equation from a graph

[puregamer]

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

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

[maggiemagnet]

What regression tools did they give you for this? Are you supposed to use Excel, your graphing calculator, or something else? Whatever tool you use, try different sorts of models (polynomial, logarithmic, etc) and compare the value of r or R² or something, so you can tell for sure which model is the "best" fit.