The growth rate of population of a city is known to be equal to 20% of the current population.Express the problem as a differential equation and find the time it takes for the population to double.The initial population of the city was 200,000 .Time is measured in years.

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

A:

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: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

A:

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: The spread of a rumor in a group of people can be modeled by a logistic growth equation. In a…

A:

Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: Consider the radioactive decay of an isotope is given by  and the solution of this differential…

Q: y = ce2t + Cze -3t y = ce-t/2 + cze¯ -2t

A:

Q: Solve the differential equation: y = 3x +log P.

A: Given equation is y=3x+log P Let us consider P as a constant and then dydx=ddx(3x + log…

Q: What is the differential equation of the problem; The birth rate of the wolf population is 7 percent…

A: Here we have to form a differential equation.

Q: After t hours, the percentage of alcohol in the blood decays according to the differential equation…

A: After time t=9.555 hours....they can legally drive...for detail solution...go through the solution

Q: A city block has 10 pigeons and then 1 week later there are 15 pigeons. Assuming the rate of growth…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: The isotope thorium-234 has a half-life of 24.5 days. (a) What is the differential equation…

A:

Q: When predicting population growth, demographers must consider birth and death rates as well as the…

A:

Q: If the number of sales is inversely proportional to the price of a product, write the differential…

A:

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: - 1 - 1 dx ?

A:

Q: -y'-11ly 0

A: Given differential equation is y''-y'-11y=0

Q: In the given question ,, determine whether the statement is true or false. If it is false, explain…

A: Given :                The function y = 0 is always a solution of a differential equation that can…

Q: Find a differential equation whose general solution is y = cet + c₂e-4² = 0

A:

Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

A: This question is about application of differential equation

Q: The differential equation for a freee-falling mass m near the surface of the earth is given by:…

A: Consider the equation:

Q: Suppose that the population P(t) of a country satisfies the differential equation = kP(900 – P) with…

A: Assume 1960 is the starting year and the population, P is in millions. So, at t=0 the value of P…

Q: An infectious disease is spreading at rate proportional to the number of people with the disease, or…

A: Given C= initial value= 118  For t=8, P=358 We have to find k

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: Calculate whether the differential equation is exact or not and Find the general solution.

A: The given differential equation is:x2+2x+ydx+2dy=0We need to check whether the equation is exact or…

Q: A constant-stirred tank reactor (CSTR), initially filled with 20 kg of salt, is diluted with enough…

A: dSdt = 180s +40 S = salt concentration = 20kg s = 1% of original amount = 1% of 20 = 0.02kg

Q: 3 y 1-x y'- 1- X y= e-e

A: Here the given differential equation is y''+1-xxy'-1x2y=ex-e-x This is a linear second order…

Q: Suppose that the population P(t) of a country satisfies the differential equation= = kP(800 - P)…

A: Given data, Population of a country satisfies the diffrential equation, dPdt=kP800-P In 1960…

Q: A dead body was discovered shortly before midnight. At exactly midnight, the temperature of the body…

A: Let T be the temperature of the object after t hours and Let Ts be the temperature of the…

Q: Q1\ A 200°F cup of tea left in 65°F room. At time initially the tea is cooling at 5 °F per minute.…

A: The rate of cooling is directly proportional to the rate of temperature difference between the…

Q: The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are…

A: Given Half of the original number of radioactivenuclei have undergone disintegration in a period of…

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 culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to be…

A: given: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to…

Q: Suppose that in a certain company, the relationship between the price per unit p of its product and…

A:

Q: If the rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where…

A:

Q: The capacity of the theater is 500 people. At a certain time, the number of people in the theater is…

A: The capacity of the theater is 500 people. At a certain time, the number of people in the theater is…

Q: Suppose that news spreads through a city of fixed size of 800000 people at a time rate proportional…

A: Total number of people in the village are =800000. No. of people who have heard the news after t…

Q: The intensity I of light at a depth of x meters below the surface of a lake satisfies the…

A:

Q: A radioactive isotope decays at a rate proportional to the amount of the isotope, in other words…

A: Given,  k = -0.283033 , let initial amount = C= 1 , final amount =A=0.5  We have to find t

Q: In a nursery, the reason for spreading a virus epidemic is equal to half of those who have not…

A: Number of children infected N w.r.t to time t in days dNdt=N Use variable saprable method to solve…

Q: The rate of growth of wild horses is proportional to 2000 – H, where H is the number of horses and…

A:

Q: Barbara weighs 60 kg and is on a diet of 1600 calories per day, of which 850 are used automatically…

A:

Q: What does it mean for a function to be a solution to a differential equation?

A: A function is said to be a solution of differential equation if it satisfies the differential…

Q: A culture initially has P0 number of bacteria. At 1 h the number of bacteria is measured to be…

A: Let P(t) be the number of bacteria present at time t.Given that the growth rate is proportional to…

Q: A 50 gallon tank is full to the brim with pure water, and 5 gallons/minute of a brine solution with…

A: Let s(t) be the amount of salt (in kg) in the tank at time t. Now, given that salt is entering in…

Q: A 100,000 liter tank of pure water was accidentally mixed with a 7000 liters of salt with a…

A:

Q: A bowl is removed from a pottery kiln at a temperature of 200 degrees Celsius and placed on a rack…

A:

Q: After a murder has been committed, the body, which was originally at 37°C, cools according to…

A:

Q: A body at a temperature of 50° F is placed outdoors where the temperature is 100° F. If after 5…

A:

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.