Rational Exponents.
\begin{equation*}
a^{m/n} = (a^{1/n})^m = (a^m)^{1/n},~~~~a \gt 0\text,~~ n \ne 0
\end{equation*}
Animal | Bat | Squirrel | Raccoon | Lynx | Human | Moose | Rhinoceros |
Weight (kg) | \(0.1\) | \(0.6\) | \(8\) | \(30\) | \(70\) | \(360\) | \(3500\) |
BMR (kcal/day) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) | \(\) |
Animal | Bat | Squirrel | Raccoon | Lynx | Human | Moose | Rhinoceros |
Weight (kg) | \(0.1\) | \(0.6\) | \(8\) | \(30\) | \(70\) | \(360\) | \(3500\) |
BMR (kcal/day) | \(12\) | \(48\) | \(333\) | \(897\) | \(1694\) | \(5785\) | \(31,853\) |
\(x\) | \(0.1\) | \(0.2\) | \(0.5\) | \(1\) |
\(f (x)\) |
\(x\) | \(2\) | \(5\) | \(8\) | \(10\) |
\(f (x)\) |
\(x\) | \(0.1\) | \(0.2\) | \(0.5\) | \(1\) |
\(f (x)\) | \(5.623\) | \(3.344\) | \(1.682\) | \(1\) |
\(x\) | \(2\) | \(5\) | \(8\) | \(10\) |
\(f (x)\) | \(0.595\) | \(0.299\) | \(0.210\) | \(0.178\) |
Weight (grams) | \(97.5\) | \(92.5\) | \(85\) | \(80\) |
Hours since eating | \(\) | \(\) | \(\) | \(\) |
Point on graph | \(A\) | \(B\) | \(C\) | \(D\) |
\(t\) | \(5\) | \(10\) | \(15\) | \(20\) |
\(I(t)\) | \(\hphantom{00000} \) | \(\hphantom{00000} \) | \(\hphantom{00000} \) | \(\hphantom{00000} \) |
\(t\) | \(6\) | \(10\) | \(14\) | \(20\) |
\(N(t)\) | \(\hphantom{00000} \) | \(\hphantom{00000} \) | \(\hphantom{00000} \) | \(\hphantom{00000} \) |
\(A\) | \(10\) | \(100\) | \(1000\) | \(5000\) | \(10,000\) |
\(S\) | \(\hphantom{000000} \) | \(\hphantom{000000} \) | \(\hphantom{000000} \) | \(\hphantom{000000} \) | \(\hphantom{000000} \) |
River | Area of drainage basin |
Length |
Amazon | \(2,700,000\) | \(4300\) |
Nile | \(1,400,000\) | \(4200\) |
Mississippi | \(1,300,000\) | \(4100\) |
Yangtze | \(580,000\) | \(2900\) |
Volga | \(480,000\) | \(2300\) |
St. Lawrence | \(460,000\) | \(1900\) |
Ganges | \(440,000\) | \(1400\) |
Orinoco | \(380,000\) | \(1400\) |
Indus | \(360,000\) | \(2000\) |
Danube | \(350,000\) | \(1800\) |
Colorado | \(250,000\) | \(1700\) |
Platte | \(72,000\) | \(800\) |
Rhine | \(63,000\) | \(900\) |
Seine | \(48,000\) | \(500\) |
Delaware | \(12,000\) | \(200\) |
Variable | Exponent, \(p\) |
Home range size | \(1.26\) |
Lung volume | \(1.02\) |
Brain mass | \(0.70\) |
Respiration rate | \(-0.26\) |
\(b\) | \(65\) | \(110\) | \(170\) | \(205\) | \(300\) | \(360\) | \(615\) |
\(C\) | \(6\) | \(15\) | \(30\) | \(40\) | \(68\) | \(110\) | \(240\) |
Year | Cumulative miles redeemed (billions) |
\(1982\) | \(14.8\) |
\(1984\) | \(85.3\) |
\(1986\) | \(215.4\) |
\(1988\) | \(387.5\) |
\(1990\) | \(641.3\) |
\(1992\) | \(975.2\) |
\(1994\) | \(1455.9\) |
\(1996\) | \(1996\) |
\(1998\) | \(2670.8\) |
\(2000\) | \(3379.1\) |
\(2002\) | \(4123.6\) |