A very nonlinear system of three equations
Here's a fun little problem: determine the exponential curve f(x) = c + ba^x defined by three points, (2,10), (4,6), and (5,5).
The system of three equations and three unknowns is
10 = c + ba^2
6 = c + ba^4
5 = c + ba^5
It's not that hard to solve numerically. With a little algebraic substitution and iteration, the answer turns out to be
a = 0.640388203
b = 16.53456516
c = 3.219223594
But is there a more elegant way to use Sage to arrive at this result? I'm stumped.