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## Related Calculus Q&A

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Q: 2. A radioactive material loses 25% of its mass in 10 minutes. What is its half-life?

A: Let No be the initial mass, N be remainingmass. Then N= No - 25100 No = No - No4=34NoHence t…

Q: 7. A radioactive material decays at a rate proportional to its amount. If the material has a…

A: Click to see the answer

Q: 6. A sample of tritum-3 decayed to 94.5% of its original amount after a year. (a) What is the…

A: A sample of tritum-3 decayed to 94.5% of its original amount after a year. Note: Multiple…

Q: 2-Suppose that the half-life of a certain radioactive substance is 2 days and there are 50g…

A: After each half life the amount left will be half the initial amount.

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: 1. Radium decomposes at a rate proportional to the amount present. In 100 yrs, 100 mg of radium…

A: It is given that the rate of decomposition rate of radium is proportional to amount present. Let the…

Q: 1. Radium decomposes at a rate proportional to the amount present. In 100 yrs, 100 mg of radium…

A: Given that Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of…

Q: A radioactive sample has a decay constant of 0.2193/min. (a) What is its half-life? (b) If at the…

A: The equation of the radio activity is N=N0e-λt where, N is the number of atoms left, N0 is the…

Q: A scientist wants to determine the halflife of a certain radioactive substance. She determines that…

A: The half life function is given by: N(t)=N0(0.5)t/t1/2 where N(t) is the final amount in milligrams…

Q: 1. A sample of einsteinium-252 decayed to 64.3% of its original mass after 300 days. a) What is the…

A: Let 100 be the original mass 64.3% of 100 is 64.3100 of 10064.3100·100=64.3 Now we find out decay…

Q: 3. A radioactive substance has a half-life of 1620 years. If its mass is now 4 grams, find the time…

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Q: 3. Radioactive carbon-14 fossil decays at a rate proportional to its amount present and has a…

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Q: A sample of einsteinium-252 decayed to 64.3% of its original mass after 300 days. a) What is the…

A: Click to see the answer

Q: 3. A 90 g sample of plutonium-238 has a half-life of 88 years. How long will it take for this sample…

A: Given data: The initial weight of the sample is A0=90 g. The final weight of the sample is Af=40 g.…

Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

A: Given: dAdt=k 0.043% of total amount has disintegrated : =100-0.043%…

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

A: Click to see the answer

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: 6. Determine the initial amount of radioactive substance if after 22 years, the remaining…

A: To find the initial amount of radioactive substance, decay rate and half-life of the substance.

Q: 4.A radioactive substance loses 3% of its substance every 5 years. What is the half-life of this…

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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…

A: Click to see the answer

Q: What is the half-life of a radioactive substance if it takes 5 years for one-third of the material…

A: We have to find half life period

Q: 1. The population of Kuhala Island doubles every 3 decades. 2. The amount of radioactive isotope of…

A: Whether each given is an exponential function, exponential equation, or exponential inequality or…

Q: 3.When a living organism dies,its carbon 14 decays.The half life of carbon -14 is 5,730 years.If a…

A: Click to see the answer

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: 9. If 75 mg of a radioactive substance decays to 15 mg in 20 years, find the Half-Life, in minutes,…

A: Click to see the answer

Q: 4. Radium decomposes at a rate proportional to the amount present. If half the original amount…

A: Solve differential equation

Q: 1. The amount of a certain medicine in the bloodstream decays exponentially with a half- life of 5…

A: Here, given that the amount of certain medicine in the bloodstream decays exponentially with a…

Q: suppose a sample of a certain substance decayed to 77.2% of its original amount after 300 days. (two…

A: Let t = time in daysN(t) =remaining quantity of certain substance at any time 't'No…

Q: 4. How much should be invested at 12.5% compounded continuously to end up with $1000 at the end of 5…

A: Click to see the answer

Q: 1. How much time is needed for a sample of Pd-100 to lose 93.75% of its original amount? Pd-100 has…

A: We need to find the time required for a sample of Pd-100 to lose 93.75% of its original amount. To…

Q: If we start with 1.000 g of strontium-90, 0.953 g will remain after 2 years. (a) What is the…

A: Click to see the answer

Q: 21. Strontium-87 is used in the study of bones. After one hour, 78.1 mg remains of a 100 What is the…

A: Radioactive decay follows the first-order kinetics. To calculate the half-life of Strontium-87 first…

Q: Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

A: Click to see the answer

Q: What is the third-life of Woosterium-21? That is, find the time it takes a sample of Woosterium-21…

A: Exponential Decay Law A=A0e-kt t - time A - amount of sample after time t A0 - amount of sample at…

Q: What is the half-life of tritium, which decays at a rate of 5.471% per year.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose a sample of a certain substance decayed to 65.8% of its original amount after 300 days. (Ro…

A: Given that the substance decayed to 65.8% of its original amount after 300 days. (a) To determine…

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

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: An initial population of 8,000 decays for two years until the population is 500. By what percentage…

A: Given- An initial population of 8,000 decays for two years until the population is 500. To…

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

A: Click to see the answer

Q: Find the half-life of a radioactive substance that decays at a continuous rate 19% per minute.

A: We have to find the half-life of a radioactive substance that decays at a continuous rate 19% per…

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

A: Click to see the answer

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

A: Click to see the answer

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

A: The information provided in the problem are as follows: Given conditions: How long does it take for…

Q: Ununoctium decays naturally at the rate proportional to the original quantity. If there are 20 grams…

A: Click to see the answer

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

A: Click to see the answer

Q: 8) A bacterial culture has an initial population of 10,000. If its population declines to 3000 in 8…

A: Exponential model of population is given by, P(t) = Po * e^(kt).