Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 320 grams,how long would it be until the mass of the sample reached 250 grams, to the nearest tenth of a year

Q: Suppose a scientist has a fossil sample with 180 g (grams) of carbon-14. If its original amount of…

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Q: The half-life of strontium-90 is 28 years. How long will it take a 56 mg sample to decay to a mass…

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Q: If the population of a small city is 45,000. If the population grows continuously by 5% per​ year,…

A: Here we use compound interest based formula. If p is present population, r is rate of growth of…

Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given: Half-life of radium = 1590 years To find: Time taken to disappear 1/4 of the radium. Formula…

Q: A certain bacterium is known to grow according to the Malthusian model, doubling itself every 8…

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Q: An element with mass 140 grams decays by 21.6% per minute. How much of the element is remaining…

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Q: The half-life of substance X is 3.5 years.  How long will it take for a 96.0 mg sample of substance…

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Q: A bacteria population grows by 10% every 3 days. Based on this, if we initially have 2,000…

A: First of all we should know that the growth is exponential so formula will be: Nd = N0ekd where N0…

Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given that Half life of radium is 1590 years To find How long would you have to wait for 1/8 of it…

Q: The amount of carbon 14 remaining in a sample that originally contained A grams is given by C(t) =…

A: The amount of carbon 14 remaining in a sample that originally contained A grams is given bt…

Q: If a piece of charcoal made from wood of a tree shows only 62% of the carbon 14 expected living in…

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Q: A certain hermit wants to design a reactor using radioactive material A that will be converted into…

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Q: If 14 g of a radioactive substance are present initially and 3 yr later only 7 g remain, how much of…

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Q: A sample of tritium-3 decayed to 85% of its original amount after 4 years. How long would it take…

A: Given problem:- A sample of tritium-3 decayed to 85% of its original amount after 4 years. How long…

Q: A sample of a newly discovered element, West Virginium, has a half-life of 170 years. How long will…

A: We have to find the time required.

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: A sample of radium has a weight of 1.5 mg and a half life of approximately 6 years. How much of the…

A: Given Data: The weight of the sample of radium is: W=1.5 mg The approximate half-life of the sample…

Q: The half life of a certain isotope is 8.5 hours. If we have a sample of 10 ounces of that isotope,…

A: Consider the following information: Half life periodt12=8.5 hours Decay constantλ=ln2t12=ln28.5…

Q: If 525 mg of a radioactive element decays to 450 mg in 48 hours, what is its half-life?

A: we are using model for radioactive decayN=N0e-λtwhereN0=initial amountN=The amount test of a…

Q: How long does it take for 90% of a given quantity of the radioactive element cobalt-60 to decay,…

A: Radioactive element decay rate.

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

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Q: An isotope Of thorium has a half-life Of 18.4 days. To the nearest day, how long will it be until…

A: Given half life = 18.4 days

Q: Element X is a radioactive isotope such that every 4 years, its mass decreases by half. Given that…

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Q: 4. The half-life of carbon-14 is approximately 6000 years. How much of 800 g of this substance will…

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

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Q: Suppose you have 100g of Titanium-44, which has a half-life of 63 years. After how long will only 1g…

A: Initial amount=P=100  Half life= H= 63 years  Final amount= A= 1  Time= t years Using the half-life…

Q: A certain radioactive isotope has a half-life of approximately 1750 years. How many years to the…

A: Consider the amount is, A=Pert here, A is the isotope, P is the initial amount and r is the…

Q: Suppose the half-life of a certain radioactive substance is 20 days and that there are5 grams…

A: Given that, The half-life of a certain radioactive substance is 20 days and that there are 5 grams…

Q: 2. Suppose a nuclear accident releases 50 kilograms of the element Cesium 137. If the half life of…

A: Given- Intial amount of Cesium-137 is 50 kg and half life is 30 years. To find- The amount after 30…

Q: A certain element decays at a rate of .000163/year. Of a piece of this element of 450 kg, how much…

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Q: The population of one state increases at a rate numerically equal to the cube root of the…

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Q: Element X decays radioactively with a half life of 9 minutes. If there are 170 grams of Element X,…

A: Given- Element X decays radioactively with a half life of 9 minutes and there are 170 grams of…

Q: How many half lives must have passed for an isotope with a half life of 10 years to decay from 1600…

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

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Q: half life of a decaying substance is the amount of time it takes for the substance to reduced to…

A: Given query is to find the the time taken to reduced the substance to 10 mg.

Q: Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000…

A: Given that the half life is 1000 years. This means 1/2 of the the original amount is left after 1000…

Q: If 14 g of a radioactive substance are present initially and 8 yr later only 7 g​ remain, how much…

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Q: If the population of a small city is 55,000. If the population grows continuously by 5​% per​ year,…

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Q: A radioactive substance has a half-life of 25 years. If 640 grams of the substance are present…

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Q: Suppose you have a cache of radium, which has a half-life of approximately 1590 years. How long…

A: Given, you have a cache of radium, which has a half-life of approximately 1590 years.

Q: 22. The half-life of radium-226 is 1620 years. a) If the current mass of a sample is 100 grams, what…

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Q: If 12 g of a radioactive substance are present initially and 8 yr later only 6 g​ remain, how much…

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Q: If 16 g of a radioactive substance are present initially and 9 yr later only 8 g​ remain, how much…

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Q: If 16 g of a radioactive substance are present initially and 5 yr later only 8 g​ remain, how much…

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Q: The half life of a decaying substance is the amount of time it take for the substance to reduced to…

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Q: Element X is a radioactive isotope such that every 27 years, its mass decreases by half. Given that…

A: Radioactive decay

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

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Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

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Q: Element X decays radioactively with a half life of 9 minutes. If there are 760 grams of Element X,…

A: Formula for half life is as below : N(t)=19 gramsN0=760t = ?t12=9 minutes

Q: Element X decays radioactively with a half life of 8 minutes.If there are 980 grams of Element X,…

A: We have to find the time

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.