(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: 9780135240687

Author: Lial

Publisher: PEARSON

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.3, Problem 42E

Chapter 13.3, Problem 44E

Students have asked these similar questions

Peggy conducted a study to identify the randomness of rainy days in fall. For 15 days, she recorded whether it rained that day or not. They denoted a rainy day with the letter R, a day without rain with the letter N. R N N R R N N R R N N R R R R Test the sequence for randomness. Use .

Consider the grades for the math and history exams for 10 students on a scale from 0 to 12 in the following table. Student Math History 1 4 8 2 5 9 3 7 9 4 12 10 5 10 8 6 8 5 7 9 6 8 9 6 9 11 9 10 7 10 Compute the Spearman correlation coefficient. Round your answer to three decimal places.

Q4 3 Points 1 Let A = 2 3 7 5 11 Give one nontrivial solution X of the homogeneous system Ax = 0. (Your vector x should have explicit numbers as its entries, as opposed to variables/parameters). Show your work for how you found it. Please select file(s) Select file(s) Save Answer

Chapter 13 Solutions

MATHEMATICS WITH APPL....-ACCESS

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

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.