One model for the way diseases die out when properly treated assumes that the rate dy/dt at which the number of infected people changes is proportional to the number y. The number of people cured is proportional to the number y that are infected with the disease. Suppose that in the course of any given year, the number of cases of a disease is reduced by 20%. If there are 10,000 cases today, how many years will it take to reduce the number to 1000?

Q: Given the rate of change of a quantity Q and its initial value Q(0), explain how to find the value…

A: Given: the rate of change of a quantity Q and its initial value Q(0), To find: the value of Q at a…

Q: Over 4 years, researchers studied the growth of a fish population and found its growth rate to P'(t)…

A: hintddxtan-1x=11+x2 or,∫11+x2dx=tan-1x

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Given that ,    Ecologist estimate that, when the population of a certain city is x thousand…

Q: A bacterial population is 7000 at time t = 0, and its rate of growth is 1,000 · 4t bacteria per hour…

A: It is given that at t=0 bacteria population is 7000   The growth rate is 1000*4t

Q: Suppose that y = y(t) is the size of a population at time t and that the rate of change of the size…

A: Given that the rate of change of size of the population is proportional to the square of the current…

Q: Initially 50 grams of radioactive substance was present. After 6 hours the mass had decreased by 9%.…

A:

Q: ologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Answer

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Solve for the value

Q: It is known that the population of a certain country at time t is proportional to the people living…

A:

Q: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

A: Given: Initial value, R0=1400 counts/min Ending value, R = 1000 counts/min Time that has passed, t =…

Q: Suppose that the fish population P(t)in a lake is attacked by a disease at time t=0, with the result…

A: From the given data, dPdt=βt-δtPβ=0δ=kPP0=100,000P20=1984Px=0x=?

Q: For any logistic equation, show that the point of inflection occurs at y = L/2 when the solution…

A: Given: The logistic equation

Q: A population of mites growsat a rate proportional to the number present, y. If the growthconstant is…

A: Assume population at time t is p Let f(t)=population at time t=p

Q: The natural law of decay is used to study the radioactive decay of Radium: dm = -km dt Where m is…

A: This question is related to differential equations, we will solve it using given information.

Q: A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial…

A:

Q: If population y grows at a rate proportional to the current population, then y could be

A: This make separable differential equation

Q: A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present.…

A: We are given that: The radioactive element decays at rate 5% annually and there are 40 g substance…

Q: Assume that in a certain country, the rate at which jobs are created is proportional to the number…

A: Explanation: Suppose that number of jobs  = N Here given that, the rate at which jobs are created is…

Q: A bacterial population B is known to have a rate of growth proportional to B itself. If between noon…

A: We will use the exponential growth equation of bacteria .

Q: A bacteria colony grows at a rate of 11% per year. If the initial sample has a mass of 500 grams,…

A: We are given that the grow after each year is 11%, that means if the initial value is x, then the…

Q: The natural law of decay is used to study the radioactive decay of Radium: dm -km dt Where m is the…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given : A town predicts that its public school population will decrease at the rate of

Q: An environmental study of a certain community suggests that t years from now the level L(t) of…

A:

Q: Solve for when the population increases the fastest in the threshold logistic equation : 1000 P'(t)…

A:

Q: Initially there was 80 milligrams of radioactive substance present.  After an 8 hour period the mass…

A: From the differential equation from the given information. dPdt=kPdPP=kdt Here, the amount of…

Q: a. A tank holds 1000 liters of water, in which 15 kg of salt is dissolved. Pure water enters the…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given,           Because of job outsourcing, a town predicts that its public school population will…

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: Suppose that a community contains 15,000 people who are susceptible to Michaud’s syndrome, a…

A:

Q: ) An environmental study estimates that t years from now, the level of carbon monoxide in the air of…

A: Given that :-the level of carbon monoxide:Q(t)=0.01t3+0.1t+2.2 ppm.Q(5)=0.01(5)3+0.1(5)+2.2…

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present.…

A:

Q: The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: g) For how long do we have to invest $1000 at a rate of 2.5% compounded continuously to obtain a…

A:

Q: (b) If n'(t) is the growth rate of a bee population in bees per week, what does n'(t)dt represent?

A: Given,n'(t)=growth rate of bee populationt=time in weeks

Q: A bacterial population B is known to have a rate of growth proportional to B itself. If between noon…

A: Solved below

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A:

Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: Two substances, A and B, are being converted into a single compound C. In the laboratory it has been…

A:

Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: Given that, The half-life of a radioactive material whose rate of disintegration is proportional to…

Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

A:

Q: Initially 48 grams of radioactive substance was present. After 6 hours the mass had decreased by…

A:

Q: A culture initially has N0 number of bacteria. At time t = 1 hour the number of bacteria is measured…

A:

Q: Solve for when the population increases the fastest in the threshold logistic equation : 1000 P'(t)…

A:

Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: The population of Normal, Illinois grows proportionally to its population at time t. At an initial…

A: Given, dPdt=kP Where P is the population and k is the proportionality constant.

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: .

Q: A team of biologists stocked a lake with 100 fish of one species to conduct an experiment. They…

A: Given that initial number of fish is 100 and rate of increase of population of fish is directly…

Q: Suppose there is a population of rabbits that (when left alone) experiences population growth at a…

A: Proportionality is between two variables when when they yield fixed ratio, with certain constant…

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.