To find the instantaneous rate of growth of the culture at 3 minutes, we need to find the derivative of the function f(t) with respect to t and evaluate it at t = 3.

The derivative of f(t) = 81t^3 + 90 is given by:

f’(t) = 3 * 81t^2

Evaluating this derivative at t = 3:

f’(3) = 3 * 81(3)^2 = 3 * 81 * 9 = 2187

Therefore, the instantaneous rate of growth of the culture at 3 minutes is 2187 milligrams per minute.