1. Initially, there are 150 grams of radioactive element and in 2550 years there will be 60 grams left. a) Determine the exponential decay equation for this element. b) How long will it take for half of element to decay? Give the answer to the nearest whole number.

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: 100mg sample of tritium-3 decayed to 94.5mg after a year. (i) What is the half-life of tritium-3?…

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Q: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

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Q: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

A: The radioactive element​ carbon-14 has a​ half-life of 5750 years, then the decay constant λ by…

Q: A sample of a newly discovered element, West Virginium, has a half-life of 425 years. How long will…

A: Given: half lifet12 of element is 425 years, initial weightA0 is 803mg and after decay is 401.5mg.…

Q: Suppose a sample of a certain substance decayed to 77.4% of its original amount after 300 days.…

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Q: 10. Oscar invests $46,200 in an account that earns 3.675% interest, compounded continuously. How…

A: Given , Oscar invested amount 46,200 dollars .             Interest is 3.675% it is compound…

Q: en artifact found in a crypt contains 93 percent of the carbon-14 that is present in living flax. To…

A: Given that a linen artifact found in a crypt contains 93 percent of the carbon-14 that is present in…

Q: If half a certain amount of radium decays in 1600 years. What percentage of the original amount will…

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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: 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: 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: 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: If radio active carbon-14 has a half -life of 5750 years ,what will remain of one gram after 3000…

A: The formula for the half-life is given by Nt=N012tt12 where N(t) is the amount of substance…

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

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Q: If the half-life of a radioactive substance is 7,600 years, then at what rate is it decaying? 1…

A: We can find the rate of decay as below.

Q: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

A: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

Q: 4. Te- 105 has a half life of 203.9 hours. If there are 1054 g of Te - 105 initially, how long will…

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Q: 1. Suppose that a couple invested P50, 000 in an account when their child was born, to prepare for…

A: NOTE: As Per our guidelines, I have solved first problem.   P be principal amount A be the final…

Q: 2. Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

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

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

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Q: A certain substance decays so that each year 92% of the previous year's material is still present.…

A: A substance decay such that each year 92% of the previous year's material still remains. So, 8% of…

Q: If Sandago has a present population of 70,000 and the population is increasing by 3% each year. 1.…

A: The function that models the population at time t is given by, Pt=P0ert, where P0 is the initial…

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: A sample of a newly discovered element, West Virginium, has a half-life of 295 years. How long will…

A: We have to find out t

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

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Q: If 275 mg of a radioactive element decays to 200 mg in 48 hours, what is its half-life?

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Q: Solve the problems.

A: Q=Pert In this example: P=$ 3500, Q=$ 10,500, r=9%p.a. Using the formula above:10500=3500e0.09t…

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: The radioactive element carbon-14 has a half life of 5750 years. A scientist determined that the…

A: Given:The radioactive element carbon-14 has a half-life of 5750 years and the bones from a mastodon…

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: Only 25% of the carbon-14 in a wooden bowl remains. How old is the bowl? (Carbon-14 has a half-life…

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Q: The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that a…

A: The half life is 5750 years. Amount of carbon-14 lost is 28%.

Q: suppose we put $2000 into an account earning 10% interest compounded continuously. how long will it…

A: $2000 into an account earning 10% interest compounded continuously

Q: The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the…

A:

Q: An element with a mass of 120 grams decays by 27.5% per minute. What is the exponential equation…

A: Let us suppose that the initial mass of the element is M0 Let the mass after time t minutes be Mt…

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

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Q: Only 40% of the carbon-14 in a wooden bowl remains. How old is the bowl (rounded to the nearest…

A: Consider the given informationRemaining amount of carban-14 = 40%Now The radioactive decay equation

Q: The half-life of carbon-14 is 5730 years. How long does it take for 2.1 grams of carbon-14 to be…

A: A(t)=A0(1/2)t/h h is the half life A0 is the initial value

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

A: Consider N (t) is the amount of tritium-3 relative to the original amount, then general form is,

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

A: Let us assume it takes n half-lifes to reach 10mg

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.