   Chapter 6.2, Problem 21E

Chapter
Section
Textbook Problem

Writing and Solving a Differential Equation In Exercises 21 and 22, write and find the general solution of the differential equation that models the verbal statement. Evaluate the solution at the specified value of the independent variable.The rate of change of N is proportional to N. When t = 0 , N = 250 , and when t = 1 , N = 400 . What is the value of N when t = 4 ?

To determine

To calculate: General solution for the differential equation that models the verbal statement, ‘The rate of change of N is proportional to N’ and finding the solution for N at t=4.

Explanation

Given:

The change in rate of N is proportional to N.

For t=0 the value of N=250 and also for t=1 the value of N=400.

Formula used:

Integration of xn is given by:

xndx=xn+1n+1+C

Integration of 1x is given as,

1xdx=log|x|+C

Calculation:

As change in rate of N is proportional to N, we have:

dNdtN

By using proportionality constant k in above equation:

dNdt=kN

By multiplying both sides by dt, we get:

dNdt×dt=kNdtdN=kΝdtdNN=kdt

Next, by integrating on both sides:

dNN =kdtln|N| =kt+C1eln|N|=ekt+c1N=ekt+c1

By simplifying further,

N=ekt+c1N=ekt×ec1

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

Find the area of the shaded region.

Calculus: Early Transcendentals

In Exercises 4562, find the values of x that satisfy the inequality (inequalities). 47. 4x 20

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Factor the following.

Mathematical Applications for the Management, Life, and Social Sciences

Given: AM=4x4 MB=5x+2 AB=25 Find: MB

Elementary Geometry For College Students, 7e

Evaluate each expression: 692912+6

Elementary Technical Mathematics

Find f(x) if f(x) = 10x2 + cos x. a) 20x sin x + C b) 20x cos x + C c) 103x3cosx+C d) 103x3+sinx+C

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Determine 1+2+3.

Mathematics For Machine Technology

Why are studies that examine the effects of aging not considered true experiments?

Research Methods for the Behavioral Sciences (MindTap Course List) 