Cost as a Function of Land Pressure and Investment Count

This puzzle is solved.

Here is how cost is computed, right now (copied from the test): Given number L (= ) And number F (= ) And number I (= ) And number C (= ) And count N (= ) When investment cost R is computed based on the following: | Parameter                | Value | | empire total land        | L     | | empire used land         | F     | | investment land increment | I    | | investment cost factor   | C     | | investment count         | N     | | purchase count           | 1     | And number Expected = C * (2^(I * (F + I)/L)) * (1 + (0.01 * [count] N)^2) Then number R = Expected

The math in the comment below seems right but I can't get the formula to work. 2^((R+I)*I) = 2^(I*(R+I)) = (2^I)^(R+I) A = 2^I R = F/L R = (F0 + I*N)/L A^(R) = A^((F0 + I*N)/L) = A^((1/L)*(F0 + I*N) = (A^(1/L))^(F0 + I*N) B = 2^(I/L) = (2^I)^(1/L) = A^(1/L) A^((1/L)*(F0 + I*N) = B^(F0 + I*N) = B^(F0)*B^(I*N) = B^(F0)*(B^I)^N D = 2^(I^2/L) = (2^(I/L))^I = B^I B^(F0)*(B^I)^N = (B^F0)*D^N 2^((R+I)*I)= (B^F0)*(D^N) C(2^((R+I)I))(1+ k*N^2) = C*(B^F0)*(D^N)*(1 + k*N^2) C' = C*(B^F0) C' * D^N * (1 + k*N^2) Then take the integral of that over N and compute the area under the curve.