Solved. Thanks!
I would do that making
(1950, 554.8)
(1960, 657.5)
(1985, 1070.0)
(1995, 1220.5)
into
(0, 554.8)
(10, 657.5)
(35, 1070.0)
(45, 1220.5)
Now one by one substitute these values into the equation in post #2.
Using $\displaystyle (0, 554.8)$
$\displaystyle y = ax^3+bx^2+cx+d$ becomes $\displaystyle 554.8 = a(0)^3+b(0)^2+c(0)+d= \dots$
Using $\displaystyle (10, 657.5)$
$\displaystyle y = ax^3+bx^2+cx+d$ becomes $\displaystyle 657.5 = a(10)^3+b(10)^2+c(10)+d= \dots$