a. Explanation Given information : Given equation 100 e − x / 100 = 0.01 x 2 Formula used : By Intermediate Value theorem a continuous function f ( x ) has a solution c ∈ ( a , b ) , if f ( x ) has opposite signs at x = a , b . Proof : Given equation 100 e − x / 100 = 0.01 x 2 Let f ( x ) = 100 e − x / 100 − 0.01 x 2 ..... ( 1 ) is continuous over ( − ∞ , ∞ ) . Let x = 0 , 100 in equation ( 1 ) , we get f ( 0 ) = 100 > 0 and f ( 100 ) = 100 e − 100 / 100 − 0 b. To determine To find the solution of equation 100 e − x / 100 = 0.01 x 2 using graphing calculator and correct to three decimal places.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Question

Chapter 2.5, Problem 47E

To determine

Toprove : that the equation 100e−x/100=0.01x2 has at least one real solution.

To determine

To find the solution of equation 100e−x/100=0.01x2 using graphing calculator and correct to three decimal places.

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Chapter 2.5, Problem 46E

Chapter 2.5, Problem 48E

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Chapter 2 Solutions

Biocalculus

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Toprove : that the equation 100 e − x / 100 = 0.01 x 2 has at least one real solution.

Solution Summary: The author proves that the equation 100e-x/100=0.01x2 has at least one real solution.