A new liquid substance is developed at a lab. This new substance has a half-life of 16 hours, and we have 15 grams of it. What amount of this substance will be left by the time 36 hours have passed, in grams?

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 formula for the half - life of continuosly decaying substances is N(t) = No5". where No is the…

A: Given the formula for the half life of continuously decaying substance is Nt=N012th. Given that a…

Q: A substance currently consists of C grams, and it grows at a continuous rate of 8.2% per year. e.…

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

Q: Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool…

A: The formula  N(t) = No e(-kt)  models this decay process well, where   t     = time measured in…

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 Radium-226 is 1760 years. If a sample contains 400 mg, how many mg will remain…

A: Half life of Radium-226 1760 years Initial value- a∘=400mg Given time=2000 years n=20001760…

Q: Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool…

A: Given that the amount of free chlorine to be 2.4 parts per million.Twenty four hours later the…

Q: 12. Solve the following problems. a. A nuclear chemist starts an experiment with 512 grams of a…

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Q: Under certain water conditions, the free chiorine (hypochlorous acid /HOCI) in a swimming pool…

A: This question can be solved using the law of uninhibited decay according to which  A=A0ekt

Q: Dakota's body metabolizes caffeine at a rate of 13.1% per hour (so the amount of caffeine in…

A: Given in the question, Dakota's body metabolizes caffeine at a rate of 13.1% per hour.

Q: The population of a community grows in proportion to the population at any time t. Its initial…

A: Given data is: Initial population P=1200 R=25% Time t=8 year

Q: The population of a city is 130​,000. If the population is declining continuously by 3.2​% per​…

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Q: The formula for the half - life of continuosly decaying substances is N(t) = No , where No is the…

A: Solving the problem by the given formula.

Q: A lab currently has 70 mg of radioactive material that decays at 3.5% per year. Federal regulation…

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Q: The half-life of polonium is 139 days, but your sample will not be useful to you after 95% of the…

A: It is given days half-life of polonium is 139 days. By the definition of half life, A139=12A0

Q: The half-life of radium is approximately 1690 years. A laboratory has 50 milligrams of radium. How…

A: Given that, the half life of radium is approximately 1690 years. Use the formula N=N012n to find the…

Q: A grey squirrel population was introduced in a certain county of Great Britain 35 years ago.…

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Q: In a population of 600 robins, the per capita birth rate in a particular period is 0.06 and the per…

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Q: The half-life of carbon-14, 14C, is approximately 5,730 years. A bone fragment is estimated to have…

A: Given information: Initial amount=Q0=7 mgHalf life=t12=5730 years

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: 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: The half-life of radioactive strontium-90 is approximately 31 years. In 1960, radioactive…

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Q: Two populations of bacteria were given food treated with different vitamins to see how they would…

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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: 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: Under certain water conditions, the free chlorine (hypochlorous acid, HOCI) in a swimming pool…

A: According to the decay law/uninhibited decay law:  A=A0 ek·t, where A0 is the initial amount. Given:…

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: A certain breed of amoeba has been observed to triple its population every two minutes. How long it…

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Q: fea)=4(2 grath /decay

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Q: How much of a 102-mg sample would be remaining after 7 years? b) If the half-life were shorter than…

A: In this question, we use the application of differential equation to calculate the amount of lead…

Q: the number of bacteria in a certain population increases to a continuous exponential growth rate,…

A: NOTE: Refresh your page if you can't see any equations. . the given growth rate is  r=6.2%=0.062

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: A small metal bar, whose initial temperature was 10° C, is dropped into a large container of boiling…

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Q: A herd of 21 white-tailed deer is introduced to a coastal island where there had been no deer…

A: NOTE: Refresh your page if you can't see any equations. . take t=2 years…

Q: A person with a normal body temperature of 36 °C dies in an accident while traveling by car. The…

A: A person with a normal body temperature of 36 °C dies in an accident while traveling by car. The…

Q: 1. Fermium-253 has a half life of 3 days. If we start with 1000 mg, how much will be left after 20…

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Q: there were 60 grams of carbon-14 initially, how many grams would be remaining after 12 half-lives?

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Q: A sample of bacteria is decaying according to a half life model. If the sample begins with 700…

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Q: 2a. Assume that the world population is 6 billion people and that the birth rate is 2.25% and the…

A: Given thatworld population= 6 billionbirth rate = 2.25 %death rate = 1.25 %growth rate= birth…

Q: At time t years, an industry consumes fuel at the rate of (3t + 27) 1/3 million barrels per year.…

A: Given- An industry consumes fuel at the rate of 3t+2713. To Find- (a) the total amount of fuel the…

Q: e number of years required for a $2000 investment to double at a 10% interest rate coumpounded…

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Q: he​ half-life of polonium is 139​ days, but your sample will not be useful to you after 83​%of the…

A: The given data is: The​ half-life of polonium is 139​ days but your sample will not be useful to you…

Q: 1. How many weeks will it take to have 700 g of matter decay down to 330 g of matter if the decay…

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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: It is predicted that, t years from now, the population of a certain town will be P(t)=…

A: here t= number of years  P(t)= population in thousand the given domain is

Q: 11A The gross primary productivity of an ecosystem is 3.5 kgC/m2/year, and the energy needed by the…

A: Part(a): Given, Gross primary productivity =3.5 kgC/m2/year And energy needed for their own…

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.