claim: The Obama administration is "proposing to mine another 10 billion tons of Wyoming coal, which would unleash three times more carbon pollution than Obama's Clean Power Plan would even save through 2030."
evidence: Assuming returns are reinvested, if the returns over n {\displaystyle n} successive time sub-periods are R 1 , R 2 , R 3 , ⋯ , R n {\displaystyle R_{1},R_{2},R_{3},\cdots ,R_{n}} , then the cumulative return or overall return over the overall time period is the result of compounding the returns together: ( 1 + R 1 ) ( 1 + R 2 ) ⋯ ( 1 + R n ) − 1 {\displaystyle (1+R_{1})(1+R_{2})\cdots (1+R_{n})-1} If the returns are logarithmic returns however, the logarithmic return over the overall time period is: ∑ i = 1 n R l o g , i = R l o g , 1 + R l o g , 2 + R l o g , 3 + ⋯ + R l o g , n {\displaystyle \sum _{i=1}^{n}R_{\mathrm {log} ,i}=R_{\mathrm {log} ,1}+R_{\mathrm {log} ,2}+R_{\mathrm {log} ,3}+\cdots +R_{\mathrm {log} ,n}} This formula applies with an assumption of reinvestment of returns and it means that successive logarithmic returns can be summed, i.e.