What is the opposite of exponential growth?

If by opposite, you mean inverse : The function that reverses the x-y values of the exponential function is the natural logarithmic function ; f(x) = ln x.

As the exponential function begins with a slow increase and progresses towards infinite growth, so the natural logarithmic function increases rapidly and then slows towards a zero rate of change.

To see this on a coordinate grid, reflect the exponential function in the line y = x.

image courtesy of Wikipedia