Solve each application.

One action that government could take to reduce carbon emissions into the atmosphere is to levy a tax on fossil fuel. This tax would be based on the amount of carbon dioxide emitted into the air when the fuel is burned.

The cost-benefit equation

ln (1 - P) = -0.0034 - 0.0053x models the approximate relationship between a tax of x dollars per ton of carbon and the corresponding percent reduction P (in decimal form) of emissions of carbon dioxide.

(a) Write P as a function of x.

(b) Graph P for 0 ≤ x ≤ 1000. Discuss the benefit of continuing to raise taxes on carbon.

(c) Determine P, to the nearest tenth, when x = $60. Interpret this result.

(d) What value of x will give a 50% reduction in carbon emissions?