In a certain country the government charges tax on each litre of petrol sold to motorists. The revenue per year is R million dollars when the rate of tax is x dollars per litre. The variation of R with x is modelled by the differential equationwhere R and x are taken to be continuous variables. When x = 0.5, R = 16.8.
i. Solve the differential equation and obtain an expression for R in terms of x.
ii. This model predicts that R cannot exceed a certain amount. Find this maximum value of R.

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dR dx = R( = -0.57), X