(a) To determine The equation for the number of peoples who are uninfected at time t . Explanation Given: An island has a native population of 5000 a sailor came who carries measles that has an infection rate of k = 0.25 . Calculation: Consider t as the time ( in days ) and y as the number of individuals infected at time t . The rate of spread of the disease satisfies the following logistic equation. d y d t = k ( 1 − y N ) y The general solution of the above differential equation is as follows: y = N 1 + b e − k t ...... ( 1 ) It is given that sailor carries the disease of measles. Therefore, the initial condition is y ( 0 ) = 1 . Substitute 5001 for N , 0.25 for k , 0 for t and 1 for y in equation ( 1 ) to obtain the value of b . 1 = 5001 1 + b e − 0.25 ( 0 ) 1 = 5001 1 + b b + 1 = 5001 b = 5000 Substitute 5000 for b , 5001 for N and 0 (b) To determine The number of people still uninfected after 30 days . (c) To determine The number of people still uninfected after 50 days . (d) To determine The maximum infection rate will occur.

Calculus with Applications (11th Edition)

11th Edition

ISBN: 9780321979421

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 10.4, Problem 9E

(a)

To determine

The equation for the number of peoples who are uninfected at time t.

(b)

To determine

The number of people still uninfected after 30 days.

(c)

To determine

The number of people still uninfected after 50 days.

(d)

To determine

The maximum infection rate will occur.

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Chapter 10.4, Problem 8E

Chapter 10.4, Problem 10E

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Chapter 10 Solutions

Calculus with Applications (11th Edition)

Ch. 10.1 - Find all solutions of the differential equation . Ch. 10.1 - Prob. 2YT Ch. 10.1 - Prob. 3YT Ch. 10.1 - Prob. 4YT Ch. 10.1 - Prob. 1WE Ch. 10.1 - Prob. 2WE Ch. 10.1 - Prob. 3WE Ch. 10.1 - Prob. 4WE Ch. 10.1 - Prob. 5WE Ch. 10.1 - Find the general solution for each differential...

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