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(i) Show that the model can be written as dx/dt = kx(1-x), where k is a constant. 
Initially, the mass of B is 0.2 kg.
(ii) Solve the differential equation, expressing x in terms of k and t. 
After 15 minutes, the mass of B is measured to be 0.9 kg.
(iii) Find the value of k, correct to 3 significant figures. 
(iv) Find the mass of B after 30 minutes. 
(v) Explain what the model predicts for the mass of A remaining for large values of t.