Element X is a radioactive isotope such that every 4 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 300 grams, how long would it be until the mass of the sample reached 90 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: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A: half life problem

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

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Q: Initially, there are 1 million bacteria present in a Petri dish. After 2 minutes, there are already…

A: given: Initially, there are 1 million bacteria present in a Petri dish.  After 2 minutes, there are…

Q: Suppose that in any given year the number of cases of a disease is reduced by 20%. If there are…

A: To Determine: Suppose that in any given year the number of cases of a disease is reduced by 20%. If…

Q: If you start with 65 milligrams of Chromium 51, used to track red blood cells, which has a half-life…

A: N(t)=N0e-tln2h N0=Initial amountt=decay timeh=length of half life Initial amount= N0=65 milligrams…

Q: If the population of the earth was found to be 3.5 billion in 1970, and Is Increasing at a rate of…

A: The population of the earth was 3.5 billion in 1970,  We are to find at what year population of…

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: 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: ssume a person winks at a constant rate of (11.5 ± 1.5) winks per minute. He/she winks repeatedly…

A: To determine how long does the person's lid is closed.

Q: Suppose that some graduate students left 8 grams of a radioactive substance unattended in their…

A: Consider the quantity of a radioactive substance initially present be N0. If the half-life of this…

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 new compound called Corpium radioactively decays at the rate of -0.035% every year. If there is…

A: The decay function is given by N(t)=N0ert Now, given rate is -0.035%. So, the equation becomes…

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: Suppose we focus on two countries, EUnited and Chindia. If Chindiaą has a per capita GDP shortfall…

A: How long will it take Chindia's per capita GDP level is within 1% of EUnited's?

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: There are 5,000 wolves in the park, but their population is expected to decay at a rate of 8% per…

A: Given, initially , wolves in the park = 5000 Decay of population = 8% per year finally , wolves in…

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

A:

Q: Suppose that in any given year the number of cases can be reduced by 25% instead of 20%. a. How long…

A: Hey the given problem is solved by considering the initial number of cases to be 10000.

Q: Element X is a radioactive isotope such that every 70 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: 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: A bacteria has an initial population of 200. If after 2hrs, its population is 10 times the original…

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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 type of bacteria, given a favorable growth medium, doubles in population every 6.5 hours.…

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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: An element with mass 820 grams decays by 26.8% per minute. How much of the element is remaining…

A: We have to use exponential decay function to solve the problem

Q: It is projected that t years from now the population of a certain country will be changing at the…

A: We can solve this question as below

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: alf-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only…

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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: Suppose that a bacteria population doubles every eleven hours.  If the initial population is 2,000…

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Q: A certain radioactive isotope has a half-life of 5 days. If one is to make a table showing the…

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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: It is known that the number of trees in a small forest will decrease by 5% each year unless some new…

A: The number of objects at a time can be calculated by modelling an equation for the number of trees.…

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

A:

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: If 18g of a radioactive substance are present initially and 4 yr later only 9g​ remain, how many gs…

A: It is simple unitary method problem.

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: 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…

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.