Sergio's body metabolizes caffeine at a rate of 12.9% per hour (so the amount of caffeine in Sergio's body decreases by 12.9% each hour). If Sergio consumes a cup of coffee with 88 mg of caffeine in it, how long will it take for Sergio's body to metabolize half of the 88 mg of caffeine?  hours    If Sergio consumes an energy drink with 224 mg of caffeine in it, how long will it take for Sergio's body to metabolize half of the 224 mg of caffeine?  hours    If Sergio consumes a cup of coffee with c mg of caffeine in it, how long will it take for Sergio's body to metabolize half of the cc mg of caffeine?

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

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Q: The population of Harford County was 238,145 in 2005 and 249,558 in 2015. A) assuming the growth was…

A: Topic-basic maths

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Q: The half-life of the plutonium isotope is 24,360 years. If 10 g of plutonium is released into the…

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

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Q: A 200 gal tank is half full of distilled water. At time = 0, a solution containing 1 Ib/gal of…

A: given capacity of tank =200 gal concentration =1 lb/gal rate of enter =4 gal/min rate of withdrawn…

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: If

A:

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

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Q: The radioactive isotope gallium 67 has a biological half-life of 36 hours. If we start with 100…

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Q: In a pest-eradication program, sterilized male flies are released into the general population each…

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A:

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

A:

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…

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Q: In the 2000 U.S.​ Census, a small city had a population of 45,000. By​ 2010, the population had…

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

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Q: A sample of radium has a weight of 1.5 mg and a half life of approximately 6 years. How much of the…

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Q: The population of a certain country is known to increase at a rate proportional to the number of…

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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: A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present…

A: It is given that,a radioactive substance has a decay rate of 4% per hour. If 1000 grams of the…

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

A:

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

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Q: The city of Anville is currently home to 23000 people, and the population has been growing at a…

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Q: A bacteria has an initial population of 200. If after 2hrs, its population is 10 times the original…

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Q: Due to the large number of human tourists and a declining food supply, the blue-footed booby…

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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…

A:

Q: City A has a current population of 500,00 people and grows at a rate of 3%/year. City B has a…

A: Given  City A :-  current population(P) is  500,00 people and growth rate (r) is 3% or 0.03  City B…

Q: The population of a city is 89​,000. If the population grows continuously by 3.2​% per​ year, in how…

A:

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 drug used to relieve anxiety and nervousness has a​ half-life of 13 hours. If a doctor prescribes…

A: Given that:                        Half life of drug = 13 hrsOne 2.2 mg tablet every 21 hr

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

A:

Q: The current population of a certain small town is 4,700 and is declining at a rate of 1.7% per year.…

A: The general equation for exponential decay is A = P(1 – r)t. Where, A is final population P is the…

Q: The half-life of Fermium-253 is 3 days. If a sample initially contains 100 mg, how many milligrams…

A: Half-life Formula: Where,  N(t) = amount left after time t                N0 = Initial amount…

Q: Thorium-227 has a half-life of 18.4 days. How many days will a 100mg sample take to decay to 12.5mg?

A: Here, we need to find how many days will a 100mg sample of Thorium-227 take to decay to 12.5mg.

Q: A species of endangered tigers has a population in 2020 of about 900, and that number is expected to…

A:

Q: Thorium -227 has a half life of 18.4 days. How many days will a 100mg sample take to decay to…

A: We know that, N(t)= N(0)*(1/2)t/(t1/2) N(t) = quantity of the substance remaining N(0) = initial…

Q: Sugar dissolves in water at a rate proportional to the amount still undissolved. If there were 70 kg…

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Q: In one experimental study, the growth of a certain insects is increasing at a rate proportional to…

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Q: During a certain epidemic, the number of people that are infected at any time increases at a rate…

A: image is attched

Q: A 50-mg sample of a radioactive substance decays to 34 mg after 30 days. How long will it take for…

A: The radioactive decay is modelled using the equation: N(t)=N0e-kt, where N0 is the initial amount…

Q: The radioactive isotope gallium 67 has a biological half-life of 36 hours. If we start with 100…

A: The half life of the radioactive element is the time during which half of the radioactive element…

Q: ion of a city in 2000 was 900,000 while the at demographic studies show that each ye ile 3% of the…

A: Given,   City Suburbs of the city Population in the year 2000 900,000 400,000

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: 4. If caffeine has a half-life of 2 hrs., how many of 140 mg of caffeine remain in Mr. Moreno's…

A:

Q: The population of a certain bacteria culture was 49,271 after 15 hours had elapsed. After another 22…

A: Given that the population of a certain bacteria culture was 49,271 after 15 hours had elapsed.After…

Q: The half-life of a radioactive substance refers to the amount of time it will take for the quantity…

A: Assume the starting year to be 2015. According to the given information, N0=100t12=20

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.