This is a differential equation problem. A model for a population P(t) in a suburb is given by the initial value problem dP/dt = P((10^-1) - (10^-7)P), P(0) = 4000 where t is measured in months. What is the limiting value of the population, and at what time will the population be equal to 1/2 of the limiting value?

This is a differential equation problem. A model for a population P(t) in a suburb is given by the initial value problem dP/dt = P((10^-1) - (10^-7)P), P(0) = 4000 where t is measured in months. What is the limiting value of the population, and at what time will the population be equal to 1/2 of the limiting value?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

See similar textbooks

Related questions

Q: find the general solution for this differential equationdy/dx = e^(-y)+1

A: Find the general solution for this differential equation

Q: Shinichi Kudo discovered a dead body in a room at midnight with a temperature of 20oC. Since the…

A: From newton law of cooling we know that dTdt=kT-Ts where k is constant and Ts is the surface…

Q: The logistic model can also be changed by incorporating a constant continuous rate of decrease, such…

A: Consider the given equation. dPdt=kP1-PA-H Put x=PA in the above equation. dxdt=1AdPdt Put all the…

Q: A vertical beam of light passes through a transparent substance, the rate at which its intensity I…

A: Here we have to find intensity of the beam 15 feet below the surface.

Q: The daily rate of change of the number of Pokémonin Brentwood is proportional to the square root of…

A: Given: The daily rate of change of the number of Pokémonin Brentwood is proportional to the square…

Q: The change of Turkey's population (N) over time (t) is proportional to the current population. In…

A: Note: It is assumed that the population of 2021 is being asked this question. The general solution…

Q: The rate of change of a population of bacteria in a petri-dish can be described as the difference…

Q: The total number of reported cases of an illness in a large city tt days after the start of an…

A: Given the logistic differential equation is: y'=15600y1400-y…1 The standard form of a logistic…

Q: ccording to a recent data analysis, the amount A(t) of atmospheric pollutants in a certain city is…

Q: A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable level…

A: Given: The differential equation that governs the concentration C of the pollutant as a function of…

Q: 5. A population of butterflies is released into a den and is growing according to the logistic…

A: Logistic equation: The differential equation that describes the logistic population model is given…

Q: Q3 (a) A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable…

Q: Let y = ky(1 – n) and y (0) = 2 and y(0) = 5. %3D 10 What is k? k = 4/5 What is y(3)? y(3) =…

Q: find the differential equation of the family of logarithmic curves whose equation is Cy = ln(Cx).

Q: It is estimated that t years from now, the population of a certain town will be F(t) = 40-{8/(t+2)}.…

Q: Question 2 What is the degree of the differential equation 2³ 4² + x² ( 4 ) ³ + x²y = sin æ 3 3 By…

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

100%

This is a differential equation problem.

A model for a population P(t) in a suburb is given by the initial value problem

dP/dt = P((10^-1) - (10^-7)P), P(0) = 4000 where t is measured in months.

What is the limiting value of the population, and at what time will the population be equal to 1/2 of the limiting value?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

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

Similar questions

The total number of reported cases of an illness in a large city tt days after the start of an outbreak is modeled by the function y=F(t)y=F(t) that is a solution to the logistic differential equation dydt=15600y(1400−y)dydt=15600y(1400−y). If there are 5 reported cases of the illness initially, what is the limiting value for the total number of reported cases of the illness as tt increases?
A vertical beam of light passes through a transparent substance, the rate at which itsintensityI decreases is proportional to I(t). In clear sea water the intensity3 feet below the surface is 25% of the initial intensity0I of the incident beam. What is the intensity of the beam 15 feet below the surface? Here t is the depth of the sea in feet.Model the differential equation of this problem using some physical law and hencedetermine the required.
A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable level is only 5 x 103 part/m³. The concentration of the bacteria will reduce as fresh water enter the pool. The differential equation that governs the concentration C of the pollutant as a function of time (in weeks) is given by: Q3 (a) dC + 0.05C = 0, dt C(0) = 104 (i) Estimate the concentration of the pollutant after 15 weeks by taking a step size of 1 week. (ii) Find the absolute error if the exact solution of Q3(a)(i) is C(t) = 10*e-0.05t Activa vindows
Q3 (a) A polluted pool has an initial concentration of bacteria of 10* part/m³, while the acceptable level is only 5 x 103 part/m³. The concentration of the bacteria will reduce as fresh water enter the pool. The differential equation that governs the concentration C of the pollutant as a function of time (in weeks) is given by: dC + 0.05C = 0, dt C(0) = 10* (i) Estimate the concentration of the pollutant after 15 weeks by taking a step size of 1 week. (ii) Find the absolute error if the exact solution of Q3(a)(i) is C(t) = 10*e-0.05£
The rate of change of a population of bacteria in a petri-dish can be described as the difference between the birth rate and the death rate. If the birth rate = bx, where b is a constant and x is the number of bacteria, and if death rate= px^2, where p is a constant, answer the following questions based on the description provided. Provide the differential equation related to the rate of change of bacterial population with time based on the above given information.