A radioactive substance decays at a rate proportional to the amount present ( y(t) = yoe-rt ) If 40% of such a substance decays in 20 years, what is the half-life of the substance?

Q: Five mice in a stable population of 500 are intentionally infected at r= 0 with a contagious disease…

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

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Q: Of an initial amount of 6000 g of lead-210, how much will remain in 110 years? Lead-210 decays at a…

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Q: Initially 50 grams of radioactive substance was present. After 6 hours the mass had decreased by 9%.…

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Q: d) A population of 100 bacteria decays at a rate of 5% each day How many bacteria, y, will there be…

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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…

A: topic - exponential function

Q: Initially 56 grams of radioactive substance was present. After 8 hours the mass had decreased by 6%.…

A: Let's find.

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

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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…

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Q: 2. Radioactive isotope Carbon-14 decays at a rate proportional to the amount present. If the decay…

A: Solve for the mass after time 2.2 thousand years

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

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

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

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Q: Initially 42 grams of radioactive substance was present. After 5 hours the mass had decreased by 8%.…

A: Initial mass of radioactive substance is equals to 42 g after five  hours mass is decreased by 8%

Q: To model mortality in a population of 200 laboratory rats, a scientist assumes that the number P(t)…

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Q: The half-life of Carbon-14 is 7 years. How much of an initial 131 g sample will remain after 45…

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Q: Initially there was 80 milligrams of radioactive substance present.  After an 8 hour period the mass…

A: From the differential equation from the given information. dPdt=kPdPP=kdt Here, the amount of…

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

A: The amount remaining after hours 24 hours is 88.5 milligrams.

Q: The half-life of plutonium-241 is 13 years.  What is the decay constant?  Use the approximation…

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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…

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Q: Find the amount after 3 years if $ 1000 is invested at an intrest rate of 12% per year, compounded…

A: Given :             The amount invested is $1000.             Interest rate = 12% per year.…

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

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

A: Solution

Q: Radium decomposes approximately at a rate proportional to the amount present. If 100 g now will be…

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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 certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

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Q: Initially 53 grams of radioactive substance was present. After 6 hours the mass had decreased by 6%.…

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Q: The amount of radio active material present at time t is given by A=Aoe*t, where Ao is the initial…

A: As many Questions are given , I will solve only one: Let A0 be the initial amount. Given that a…

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: 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: Initially 100 millions of radioactive substance was present. After 6 hours the mass has decreased by…

A: Given query is to find the amount of radioactive substance after 24 hours.

Q: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

A: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

Q: In March 1976 the world population reached 4 billion. At that time, a popular news magazine…

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Q: The total number of reported cases of an illness in a large city days after the start of an outbreak…

A: According to the given information the total number of reported cases of an illness in a large city…

Q: The number of bacteria in a certain population increases according to a continuous exponential…

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Q: Initially 48 grams of radioactive substance was present. After 6 hours the mass had decreased by…

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Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

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Q: 8. Determine the half-life of the substance if an initial 150mg has decayed to 50mg in a an of 20…

A: Given query is to find half life and the time when 95% amount decayed.

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

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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.