<P> Alternatively, the E-M rule is obtained if the second - order Taylor approximation is used directly . </P> <P> For continuous compounding, the derivation is simpler and yields a more accurate rule: </P> <Dl> <Dd> (e r) p = 2 e r p = 2 ln ⁡ e r p = ln ⁡ 2 r p = ln ⁡ 2 p = ln ⁡ 2 r p ≈ 0.693147 r (\ displaystyle (\ begin (array) (ccc) (e ^ (r)) ^ (p) & = &2 \ \ e ^ (rp) & = &2 \ \ \ ln e ^ (rp) & = & \ ln 2 \ \ rp& = & \ ln 2 \ \ p& = & (\ frac (\ ln 2) (r)) \ \ && \ \ p& \ approx & (\ frac (0.693147) (r)) \ end (array))) </Dd> </Dl> <Dd> (e r) p = 2 e r p = 2 ln ⁡ e r p = ln ⁡ 2 r p = ln ⁡ 2 p = ln ⁡ 2 r p ≈ 0.693147 r (\ displaystyle (\ begin (array) (ccc) (e ^ (r)) ^ (p) & = &2 \ \ e ^ (rp) & = &2 \ \ \ ln e ^ (rp) & = & \ ln 2 \ \ rp& = & \ ln 2 \ \ p& = & (\ frac (\ ln 2) (r)) \ \ && \ \ p& \ approx & (\ frac (0.693147) (r)) \ end (array))) </Dd>

Where did the rule of 70 come from