Solve the problem.
-Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. The cost benefit is modeled by $$\ln ( 1 - \mathrm { P } ) = - 0.0025 - 0.0046 \mathrm { x }$$ where x represents the dollars of tax per ton of
Carbon emitted and P represents the percent reduction in emissions of carbon. (P is in decimal
Form.) Determine P when x = 62. Round to three decimal places.
A) -0.15
B) 1.750
C) -0.246
D) 0.25

Question

Quizplus · Accepted Answer

To find P when x = 62, substitute x = 62 into the equation and solve for P:$$\ln(1 - P) = -0.0025 - 0.0046(62)$$$$\ln(1 - P) = -0.0025 - 0.2852$$$$\ln(1 - P) = -0.2877$$Raise both sides as powers of e to get rid of the natural log:$$1 - P = e^{-0.2877}$$$$P = 1 - e^{-0.2877}$$$$P \approx 1 - 0.75$$$$P \approx 0.25$$Therefore, the percent reduction in emissions of carbon when x = 62 is approximately 0.25 or 25%.

Solve the Problem ln⁡(1−P)=−0.0025−0.0046x\ln ( 1 - \mathrm { P } ) = - 0.0025 - 0.0046 \mathrm { x }ln(1−P)=−0.0025−0.0046x

Solve the Problem $\ln ( 1 - \mathrm { P } ) = - 0.0025 - 0.0046 \mathrm { x }$