A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 mg of the material present and after two hours it is observed that the material has lost 20% of its original mass, find the mass of the material after 6 hours.

Q: A radioactive material decays at a rate proportional to its amount. If the material has a life of 30…

A: This question is based on application of differential equation.

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

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Q: The radioactive isotope Carbon-14 has a half-life of 5,730 years. Given 300 grams of C-14, what is…

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

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

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

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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: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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

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

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

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Q: A radioactive substance decays at a rate proportional to the amount present ( y(t) = yoe-rt ) If 40%…

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

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

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

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

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Q: nitially, there were 100 milligrams of a radioactive substance. After six hours, the mass decreased…

A: initially there are 100 milligrams of a radioactive substance. P=100 mg after 6 hour the mass…

Q: Element X is a radioactive isotope such that every 70 years, its mass decreases by half. Given that…

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

A: Given: A radioactive element is known to decay at a rate proportional to its present mass.…

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

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

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

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

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Q: Of an initial amount of 8000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

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Q: A radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium…

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

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

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Q: A 50 mg sample of thorium-233 decays to 44 mg after 4 min. a) Determine the half-life of…

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

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Q: A tumor is injected with 0.7 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

A: The exponential function A = P * (1 - r)t  where A is the final amount and P is your inital amount.…

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

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Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

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

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

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.