1. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Integral and Rational Exponents Sections 4.2 and 4.3

2. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Use Integral Exponents A photographer uses his knowledge of exponents to determine how to illuminate his pictures properly. A photographer has a flash which illuminates a subject with an intensity I 1 = 1000 watts/m 2 at a distance of d 1 = 1.0 m. What is the intensity at d 2 = 2.0 m? The intensity equation is: Photography with Artificial Light

3. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Use Integral Exponents Use the Intensity formula: Photography with Artificial Light The intensity at 2.0 m is 250 W/m 2.

4. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Use Integral Exponents If the distance from the flash to the subject is doubled, the light spreads out to cover four times the area. Photography with Artificial Light

5. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. A 5 kg cat burns energy, E 1 at the rate of about 54 kilojoules per hour. How much energy, E 2, does a 0.1 kg chipmunk burn per hour? Energy burn, or metabolic rate, is compared using Kleiber’s Law: where m 1 and m 2 represents the mass of each of the animals. Use Fractional Exponents Animal Metabolism

6. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Use Kleiber’s Law: Use Fractional Exponents Animal Metabolism A chipmunk burns about 2.9 kJ of energy per hour.

7. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Compare the masses of the animals: Use Fractional Exponents Animal Metabolism Compare the metabolic rates of the animals: Although the cat has 50 times the mass of the chipmunk, it burns only 19 times as much energy. The cat needs to consume 19 times as much food as a chipmunk.

8. Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Historical Notes Max Kleiber was born and educated in Switzerland as an agricultural chemist. He formulated Kleiber’s Law in 1932. His law applies to all mammals, including humans. Use Fractional Exponents Animal Metabolism Human metabolic rates average about 400 kJ per hour when resting. About 19% of this is used by the brain.