Suppose the government wants to impose a tax on fossil fuels to reduce carbon emissions. The cost benefit is modeled by $\ln ( 1 - \mathrm { P } ) = - 0.0039 - 0.0048 \mathrm { x }$, where $\mathrm { x }$ represents the dollars of tax per ton of carbon emitted and $\mathrm { P }$ represents the percent reduction in emissions of carbon. ( $P$ is in decimal form.) Determine $P$ when $x = 52$. Round to three decimal places.
A) $- 0.19$
B) $0.224$
C) $1.776$
D) $- 0.218$

Question

Quizplus · Accepted Answer

To find $P$ when $x = 52$, substitute $x = 52$ into the equation: $\ln(1 - P) = -0.0039 - 0.0048(52)$. Solve for $P$ to get $P = 0.224$.

Suppose the Government Wants to Impose a Tax on Fossil ln⁡(1−P)=−0.0039−0.0048x\ln ( 1 - \mathrm { P } ) = - 0.0039 - 0.0048 \mathrm { x }ln(1−P)=−0.0039−0.0048x

Suppose the Government Wants to Impose a Tax on Fossil $\ln ( 1 - \mathrm { P } ) = - 0.0039 - 0.0048 \mathrm { x }$