Let y(t) be the size of a colony of bacteria after t hours. Suppose the rate of growth of the colony is equal to eight times the one-half power of its present size. Solve the differential equation which models this growth and an initial condition that says that at time zero the colony is of size 100.

Let y(t) be the size of a colony of bacteria after t hours. Suppose the rate of growth of the colony is equal to eight times the one-half power of its present size. Solve the differential equation which models this growth and an initial condition that says that at time zero the colony is of size 100.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: A bacteria colony begins with a population of 120 and quadruples in size every 1.5 days. If the…

A: Given initial population = 120 So, for t=0, P=120 Using that we get: Quadruples in size every 1.5…

Q: Suppose a population grows according to a logistic differential equation model. Its population in…

A: It is given that the population in years 2000 and 2001 is 500 and 1500 respectively and carrying…

Q: A colony of bacteria is growing exponentially with growth constant k = 0.25. (a) Determine the rate…

A: Given bacteria population rate and bacteria population functions are

Q: Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where…

Q: The performance level of someone learning a skill P(t) is a function of the training time t dP and…

A: Given differential equation is dPdt=kM-Pt. where Pt is the performance level at some time t and k…

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 scientist is doing an experiment on the growth of the corona virus. He started the experiment with…

A: The model is provided as: dPdt=aP1-PK. We need to use this model and the conditions provided to…

Q: Find: (a) particular solution of the logistic differential equation that describes the growth of…

A: The logistic differential equation that describes the growth of the population of wolves in some…

Q: The solution of the differential equation (logistic growth model) dy/dt = 0.2y(50 - y) is y = /(1 +…

Q: A person planning for her retirement arranges to make continuous deposits into a savings account at…

Q: Most savings banks advertise that they compound interest continuously, meaning that the amount S(t)…

Q: An ant population grows at a daily rate of 3/10 times the current population. It is known that a…

A: Given, The number of ants die in each day (c)=36 The initial number of ants(P) =400 Let P be the…

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: Suppose you have just poured a cup of freshly brewed coffee with temperature 95°C in a room where…

Q: Suppose that news spreads through a city of fixed size of 200000 people at a time rate proportional…

Q: The population of ants in a colony grows at a rate proportional to the number of ants P present at…

A: Given that the ants grow at a rate proportional to its population P at time t. i.e. dPdt α P ⇒dPdt =…

Q: person planning for her retirement arranges to make continuous deposits into a savings account at…

A: Follow the steps.

Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Q: A person planning for her retirement arranges to make continuous deposits into a savings account at…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Consider a time-varying population that follows the logistic population model. The population has a…

Question

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Please don't provide handwritten solution ....
1. A population grows continuously at the rate of 8% per year. How long does it take for the population to double ? Use differential equation it.
Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional to the number of people who have not heard the news. (a.) Formulate a differential equation and initial condition for y(t), the number of people who have heard the news t days after it has happened. No one has heard the news at first, so y(0) the number of people who have heard the news is proportional to the number of = 0. The "time rate of increase in people who have not heard the news" translates into the differential equation dy k( |3D dt
A virus has already infected 4 million people in a country before a vaccine becomes available to the public. Once vaccination starts, the number of infected people decreases at a rate that is proportional to the cube of the number of infected people. One month later, there are still 2 million people that are infected. Let p be the number of infected people (in millions) and t be the number of months since vaccination has started. (a) Find a differential equation and initial conditions to model the situation. (b) Solve the differential equation to find pp as a function of t (c) How many people are still infected three months after vaccination starts?
In 30 min
At t=0, a 600 liter tank initially contains 50 grams of salt dissolved in 300 liters of water. Then, water that contains 2 grams of salt per liter is poured into the tank at a rate of 5 liters per minute. The solution in the tank is constantly stirred so the salt concentration is uniform at any given time t. Water leaves the tank at a rate of 2 liters per minute. Determine when the tank will overflow and create a differential equation to determine how much salt will be in the tank after 1 hour.
Write a differential equation to model this physical situation. Snow is falling at a constant rate of 3/5 in per hour. It is being removed at a constant rate of 45% of the amount of snow on the ground per hour. If we use h(t) as the height of the snow at time t, and the removal of snow began at a height of 4 in --such that h(0)=4 --what would be the equation for the rate of change of the height as a function of time?