Chapter 13.5, Problem 42E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Spread of disease** An isolated community of 1000 people susceptible to a certain disease is exposed when one member returns carrying the disease. If x represents the number infected with the disease at time

(a) If *k =* 0.001, integrate both sides to solve this differential equation.

(b) Find how long it will be before half the population of the community is affected.

(c) Find the rate of new cases, *dx/dt,* every other day for the first 13 days.

**(a)**

To determine

**To calculate:** The solution of the differential equation

Where, *x* represents the number of people infected by the disease at any time *t* (in days).

Explanation

**Given Information:**

The provided differential equation is,

**Formula used:**

A separable equation is of the form:

Integration both sides yield the solution of this equation.

According to the formula

**Calculation:**

Consider the provided differential equation,

The equation is in separable form. So, integrate both sides to get,

Now, use formula

**(b)**

To determine

**To calculate:** The time before half the population of the community is affected Where the specific community of 1000 people those are suffering from several disease is exposed when one of the member returns carrying the disease.

**(c)**

To determine

**To calculate:** The rate of new cases

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