Explanation Given information: 99 % of the population is initially uninfected and each initially infected person generates, on average two new infections. Formula Used: The model considered for this purpose is 0.99 − 2 A = 1 − A . Where A is the fraction of the population infected at the end of an outbreak . The Newton-Raphson method is a method for approximating the roots of polynomial equations of any order. In fact the method works for any equation, polynomial or not, as long as the function is differentiable in a desired interval's often become increasingly better approximations of the function's root. Calculation: First find the solutuion of the equation 0.99 − 2 A = 1 − A , use Newton’s method to solve this and thus consider f ( A ) = 0.99 − 2 A + A − 1 From the above graph it is evident that solution of the equation lies close to A = 0 and A=1 Thus use Newton’s method to find the solutions with first approximations as A = 0 and A=1 From Newton’s method a function f ( x ) and the initial approximation is, x n + 1 = x n + f ( x n ) f ' ( x n ) Substitute A 1 = 0 to the above formula; [ A 2 − 0

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.8, Problem 32E

To determine

To Calculate: An approximate percentage of the population that is infected

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Chapter 3 Solutions

Biocalculus

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An approximate percentage of the population that is infected

Solution Summary: The author explains the Newton-Raphson method for approximating the roots of polynomial equations of any order.

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To Calculate: An approximate percentage of the population that is infected

Chapter 3 Solutions