   Chapter 7.8, Problem 69E

Chapter
Section
Textbook Problem

# In a study of the spread of illicit drug use from an enthusiastic user to a population of N users, the authors model the number of expected new users by the equation γ = ∫ 0 ∞ c N ( 1 − e − k t ) k e − λ t d t where c, k and λ are positive constants. Evaluate this integral to express γ in terms of c, N, k, and λ.Source: F. Hoppensteadt et al., “Threshold Analysis of a Drug Use Epidemic Model,” Mathematical Biosciences 53 (1981): 79–87.

To determine

To evaluate:

γ in terms of c,N,k&λ.

Solution:

γ=cNλ(k+λ)

Explanation

Given:

c,kandλ are positive constants.

N- Population of Users.

Formula:

Recall from previous exercise or otherwise that if a is a positive constant then 0e-axdx=1a

γ=0cNk(1ekt)eλtdt=(cNk)[0eλtdt

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Evaluate the expression sin Exercises 116. 52535252

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Simplify: 1416

Elementary Technical Mathematics

#### True or False:

Study Guide for Stewart's Multivariable Calculus, 8th

#### Graph each ellipse. x225+y29=1

College Algebra (MindTap Course List) 