The cost-benefit equation
T=-0.623-194 In (1-p)
describes the approximate tax T, in dollars per ton, that would result in a p% (in decimal form) reduction in carbon dioxide emissions. What tax will reduce emissions 70%?
well, just plug it in.
-0.623-194 ln (1-0.70) = 232.95
To find the tax that will reduce emissions by 70%, we need to substitute the given reduction percentage (70%) into the equation and solve for T. Let's go step by step:
1. Start with the cost-benefit equation:
T = -0.623 - 194 ln(1-p)
2. Since we want to find the tax that will reduce emissions by 70% (p = 0.70), substitute the value of p into the equation:
T = -0.623 - 194 ln(1 - 0.70)
3. Calculate the value inside the natural logarithm:
1 - 0.70 = 0.30
4. Take the natural logarithm of 0.30:
ln(0.30) ≈ - 1.203
5. Substitute the value of ln(1 - p) back into the equation:
T = -0.623 - 194(-1.203)
6. Simplify the equation:
T = -0.623 + 233.582
7. Calculate the final result:
T ≈ 232.959
Therefore, the approximate tax that will reduce emissions by 70% is approximately $232.96 per ton.