Purchase Solution

Modeling using Differential Equations

Not what you're looking for?

Ask Custom Question

One model for the spread of a rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor:

a) Write a differential equation that is satisfied by y ( use k for the constant of proportionality)

dy/dt =

b) Solve the differential equation

assume y(0) = 0

y =

c )A small town has 1100 inhabitants . At 8am , 100 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor (round to one decimal place).

Hours after the beginning = have a real block with this type of questions.

Purchase this Solution
Solution Summary

Differential equations are solved.

Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Systems of First Order Differential Equations

    Thanks for using BrainMass. Systems of Differential Equations are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.

  • Modeling with Higher Order Differential Equations

    91634 Modeling with Higher Order Differential Equations Two springs are attached in series as shown in Figure 5.42. If the mass of each spring is ignored, show that the effective spring constant k ot the system is defined by I/k = I/k + I/k2.

  • Algebra Basics, Equations, and Mathematical Models

    The behavior of the differential equations depends upon whether the roots of a certain quadratic are complex or real. If they are complex, then certain behaviors can be expected.

  • Quadratic equation and variables

    The behavior of the differential equations depends upon whether the roots of a certain quadratic are complex or real. If they are complex, then certain behaviors can be expected.

  • Quadratic Equation

    The behavior of the differential equations depends upon whether the roots of a certain quadratic are complex or real. If they are complex, then certain behaviors can be expected. These are often just the solutions that one wants.

  • System Modelling - Output and State Differential Equation

    It includes explanation of system modeling, and provides state equations and conservation of law.

  • Quality factors in a software product to measure quality

    Qualitative modeling makes explicit and precise the abstraction relationship between the qualitative partial knowledge representations and the theory of differential equations.

  • Solving Differential Equations and Modeling

    121375 Solving Differential Equations and Modeling (a) Find the solution of the initial-value problem? dy/dx = cos(4x) / 3 − sin(4x), y = 6 when x = 0.

  • Systems of Differential Equations : Modeling a Battle between Two Armies

    126864 Systems of Differential Equations : Modeling a Battle between Two Armies When one models a pair of conventional forces in combat, the following system arises x1' -a -b x1 p x2' = -c -d x2 + q The unknown functions x1(t) and x2(t) represent

View More Related Solutions