How do you find an exponential equation from two graph points?

I assume you're fitting an relation of the form y = aebx.

Take the natural logarithm of both sides of the relation: ln y = a + bx (1).

Suppose your points are (-1, 7.39) and (1,0.14). Because we have a relation between the logarithms of the y co-ordinates and the x co-ordinates themselves let us replaces the y co-ordinates with their logarithms to obtain the points (-1, 2) and (1, 2). Now we can use this points to obtain two simulaneous equations in the transformed equation (1) and solve it as usual to obtain a = 1 and b = -2.

The fitted relation is y = e-2x.