a certain radioactive material is known to decay at a rate proportional to the amount present. if initially 1/2 g of the material is present and after 3 years 20 percent of the original mass has decayed, determine the amount remaining after 25 years

Q: A certain radioactive material decays at a rate proportional to the amount present. At time ?=0,…

A:

Q: The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any…

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

Q: 6. The radioactive isotope of lead, PB-209, decays at a rate proportional to the amount present at…

A: Let's find time to take 90% of the lead to decay.

Q: A certain radioactive element decomposses at a rate proportional to the amount present. If 100…

A:

Q: 3. The rate at which radioactive nuclei decay is proportional to the number of such nuclei that are…

A:

Q: The rate of decay of radium is proportional to the amount present at any time. The half-life of…

A:

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Simple rate of decay of radium problem....

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Suppose…

A: I have appended the formula used in the solution part.

Q: The decay constant for the radioactive element strontium 90 is l = .0244, where time is measured in…

A: Definition used -                            Decay equation -…

Q: Radium decomposes at a rate proportional to the quantity present. If at the end of 20 years…

A: Solution

Q: How much should be invested at a rate of 7% coumpounded continuously to produce an amount of $15,000…

A:

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

A:

Q: Of an initial amount of 5000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A:

Q: Of an initial amount of 9000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A: Apply the formula  P(t)=Po(1-r)t where, Po is the initial quantity r is the rate and t is the time.…

Q: 3. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of…

A: Given: initial mass of Radium  y0=96 mgWe know that General decay equation is y=y0e-kt…

Q: Element X is a radioactive isotope such that every 7o years, its mass decreases by half. Given that…

A: Solution : Given that element X is a radioactive isotope such that every 70 years, its mass…

Q: 1. The number of a certain type of bacteria increases continuously at a rate proportional to the…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

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

A:

Q: A certain radioactive material loses mass at a rate proportional to the mass present. If the…

A:

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A:

Q: The radioactive isotope lead has a half-life of 3.3 hours and decays at a rate proportionate to the…

A: This is a problem of differential equation and integration. Based on the given scenario first of all…

Q: 4.) The half-life of strontium-90 is 28 years. Find the rate of decay. How long will it take a 50 mg…

A:

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

A: Given:- It is known that the population of a certain country at time t is proportional to the people…

Q: The half-life of plutonium-241 is approximately 13 years. How much time is necessary for a sample…

A: The exponential formula for decay is given as: A=A0e-λt               ⋯2, where A is future amount,…

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

A:

Q: A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present…

A: It is given that,a radioactive substance has a decay rate of 4% per hour. If 1000 grams of the…

Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

A:

Q: A radioactive substance has a half life of 175 years. Find the decay constant, r, for this…

A: A radioactive substance has a half life of 175 years

Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

A:

Q: 1. For a certain radioactive element decays at a rate of 37.7% per day (tis measured in days). How…

A: We need to find time.

Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

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

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

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 130 years? Lead-210 decays at a…

A: Find much much will remain

Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: 1. The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Since you posted two questions here, i can answer only first one at a time. Please repost other…

Q: When time is measured in days, the decay constant for a particular radioactive isotope is 0.14.…

A: The decay of an object follows the exponential model  where N(t)I is the amount remaining after time…

Q: A breeder reactor converts relatively stable Uranium 238 into the isotope Plutonium 239. After 15…

A:

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

A: Solved below

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

A:

Q: 1. A certain radioactive material is known to decay at a rate proportional to the amount present.…

A:

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

A: Let y be the unconverted amount of substance A at time t. Thus, the given information can be written…

Q: In one experimental study, the growth of a certain insects is increasing at a rate proportional to…

A: Given: The growth of insects is increasing at a rate proportional to the number present. To Find:…

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

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

A: The decay rate is proportional to the amount present. So, dNdt=-λN⇒dNN=-λdt⇒∫dNN=-λ∫dt+C⇒ln…

Q: Element X is a radioactive isotope such that every 28 years, its mass decreases by half. Given that…

A:

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: 1. After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is…

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.