(a) Explanation Given data: The rate at which people are becoming infected during outbreak of the disease is approximately given by f ( x ) = 2 x e − x 7 Also, at x = 0 , F ( 0 ) = 12 . Formula used: Write the formula for integration by parts: ∫ p d q = p q − ∫ q d p Here p and q are the functions of x. Calculation: The total infected people will be the equivalent to the integral of the rate at which people being infected. Mathematically, it is expressed by following expression; F ( x ) = ∫ f ( x ) d x = ∫ 2 x e − x 7 d t Now find ∫ 2 x e − x 7 d x by integrating it by part. Let p = 2 x and d q = e − x 7 d x . Now, d p = 2 d x Find v by integrating d v . d q = e − x 7 d x q = − 7 e − x 7 Ignore the constant of integration in the above integration. Now use the above formula to find ∫ 2 x e − x 7 d x (b) To determine The total number of people who have become infected by the end of 4 weeks.

12th Edition

ISBN: 9780134773285

Author: MULLINS

Publisher: YUZU

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Chapter 13.3, Problem 43E

(a)

To determine

The function F(x) that gives number of people who have become infected by day x.

(b)

To determine

The total number of people who have become infected by the end of 4 weeks.

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Chapter 13.3, Problem 42E

Chapter 13.3, Problem 44E

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The function F ( x ) that gives number of people who have become infected by day x .

Solution Summary: The author determines the function F(x) that gives number of people who have become infected by day x.