Q1. A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there are100 milligrams of the material present and if after two years it is observed that 5 percent of the original mass has decayed, find (a) an expression for the mass at any time t and (b) the time necessary for 10 percent of the original mass to have decayed.

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A:

Q: 2. A certain radioactive material is known to decay at a rate proportional to the amount  present.…

A:

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A: Here efficiency of the workers after t hours from 9.00AM is given.  We have to find the workers…

Q: The population of a certain community is known to increase at a rate proportional to the number of…

A:

Q: A radioactive material is known to decay at the rate proportional to the amount present. If…

A: Given A radioactive material is known to decay at the rate proportional to the amount present.…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given data:   The initial value of the mass is mi=50 milligrams. The mass lost after two hours is…

Q: 2. The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: A(t) = amount remaining in t years          = A0ekt, where A0 is the initial amount and k is a…

Q: 3. A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: We row that general equation for the radio active decy is M=M0e-kt            Where "M0 " is…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: As population is proportional to present population. So we need to form a differential equation. and…

Q: The value of a computer t years after purchase is v(t) = 4000e , At what rate is the computer's…

A: we need to find rate of change with respect to time of v(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: Q1. A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Let x(t) be the amount of radioactive material which is present in milligrams after t years. Given…

Q: 2. The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: 1. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

A:

Q: 4. In a culture of yeast, the amount of active ferment grows at a rate proportional to the amount…

A: Let's work on the problem straight from the statement "the amount doubles in 1 hour": let the…

Q: 4. The population of Florida (in millions) in recent years can be approximated by p(x)%3=…

A:

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) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: 3. The population of a certain country is known to increase at a rate proportional to the number of…

A:

Q: A) The population of a country has grown at a rate proportional to the number of people in this…

A: Let the present population be P0 Then t years later the population is Pt and t years ago the…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Percentage : Percentage of the item is 100th part of the number.  It is denoted by x% or written as…

Q: certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: We will solve the radioactive decay problem.

Q: 1. The rate at which radioactive nuclei decay is proportional to the number of such nuclei that are…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: A radioactive element decays according to the function Q= Q, e", where Qo is the amount of the…

A: This question is based on exponential decay.

Q: If an amount P0 is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A:

Q: 2. It is estimated that t months from now, the population of a certain town will be changing at the…

A: This question is related to population growth, We will solve it using integration.

Q: If an amount Po is invested in the Mandelbrot Bond Fund and interest is compounded continuously at…

A: Given: dPdt=0.071P, r=7.1% and initial amount invested is P0

Q: 3. The rate of population grarth of a to the number inhabitent>. If the population of a certain…

A: topic - exponential function

Q: 1. A body at 50 degrees C cools inside a room with temperature of 30 degrees C. At what temperature…

A: Let's find.

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

A:

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Topic:-  exponential function

Q: radium decomposes at a rate proportional to the quantity of radium present. suppose that it is found…

A: Given the data :

Q: A sample of 800 g of an isotope decays to another isotope according to the function A(t) = 800…

A: We have given sample of 800 g of an isotopes decays to  another isotopes according to the function…

Q: Suppose a person with x years of eduction before seeking regular employment can expect to receive an…

A:

Q: 4. During a certain epidemic, the number of people that are infected at any time increases at a rate…

A: Here the given relation is ," People that are infected at any time increases at a rate proportional…

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A:

Q: A certain population of rabbits grows proportionally to its size. If initially there are 1000…

A:

Q: The state of decay of radium is proportional to the amount present at any time. Suppose that 400 mg…

A: Here we will find radium left after 2.5 hours and 10hours,

Q: 2- An efficiency study of the moming shift at a certain factory indicates that an average worker who…

A:

Q: It is estimated that t months from now, the population of a certain town will be changing at the…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Image is attached with detailed solution.

Q: A 5kg sample of plutonium-239 has a half-life of 21,400 years by emitting a 5.157 MeV (million or…

A: Let's find time to taken sample to degrade to 4.5kg.

Q: b) Let at time t years, an industry consumes fuel at the rate of (2t + 9) million barrels per year.…

A: Given an industry consumes fuel at the rate of 2t+912 million barrels per year. If the total supply…

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A: Given relation is: Qt=-t3+6t2+24t a). The worker's rate of production at 11 AM: So put t=3 in given…

Q: A radioactive element decays according to the function Q = Q, et, where Q, is the amount of the…

A: Given:     Q=Q0ert   where Q0 is the amount of substance at t = 0.       r=-0.00027  Q is the amount…

Q: A radioactive element decays according to the function Q=Q, e", where Q, is the amount of the…

A: We will solve the problem

Q: 3. A bowl of soup has an initial temperature of 60 degrees Celsius. The temperature decreases by 6%…

A: Initial temperature= 60 degrees temperature decreases by rate 6% each minute

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.