Consider dA/dt = -k_1A + k_{-1}B and dB/dt = k_1 - k_ {-1}B . Divide both sides of each of the differential equations by k_{-1} and define a new ("dimensionless") time variable s as s = k_{-1}t.

(a) Explain why s is dimensionless, that is, why it carries no units.

(b) Write your equations in terms of the derivatives dA/ds and dB/ds.

(c) Divide every term in the equation by the total amount M and define the new quantities a = A/M, b = B/M. Explain why these variables are "dimensionless".

(d) Simplify the equations by making the substitutions suggested in (c).You should get (for example)

db/ds = a - b

Determine what is the parameter in terms of the original parameters in the problem. Interpret what this new parameter represents.