Suppose that some graduate students left 8 grams of a radioactive substance unattended in their physics lab for a few days. Given that this substance has a half-life of 9 hours, how many grams of this substance will still be there when the students return to their lab 68 hours later?

Q: You have 10 ounces of a radioactive substance with a half-life of 5 hours. How long it be until only…

A: Solution

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: ount of asprin decays exponentiallyf(t) = Ae-ktat t = 0 ,   300 = Ae0⇒ A = 300

Q: Suppose you deposit money in an investment account that pays 5% annual interest compounded…

A: r=5%=0.05 Let P be the invested money and let it be doubled in t years.

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: We will solve the exponential model for the Aspirin decay

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: The current population of a threatened animal species is 1.4 million but it is declining with a…

A:

Q: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree…

A: Given that the​ half-life of​ carbon-14 is 5600 years and if a piece of charcoal made from the wood…

Q: A scientist begins with 225 grams of a radioactive substance. After 300 minutes, the sample has…

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Q: A certain bacterium is known to grow according to the Malthusian model, doubling itself every 8…

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Q: In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear…

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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: A new water pump has a capacity of 60 m³/day. If its capacity goes down by 15% every year, in how…

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

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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: The current population of a threatened animal species is 1.7 million, but it is declining with a…

A: Given:  The current population of a threatened animal species is 1.7 million, but it is declining…

Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

A: Given:    Half-life of radioactive cobalt =5.27 years    The proportion p that remains after y years…

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: This year there were 25,000 new births in a large county, but new births are expected to decay…

A:

Q: The half-life of carbon-14 is known to be 5720 years. Doctor Frankenstein has 300 grams of…

A: From the given data:

Q: Most smoke detectors contain a tiny amount of Americium-241, which is an artificially produced…

A: Assuming that the radioactive decay follows exponential distribution, the quantity of substance…

Q: If 250mg of a radioactive element decays to 190mg in 12 hours, find the half-life of the…

A:

Q: If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink. Iodine 131…

A: Given:- If dairy cows eat hay containing  too much iodine 131, their milk will be unfit to drink.…

Q: Suppose you have 100g of Titanium-44, which has a half-life of 63 years. After how long will only 1g…

A: Initial amount=P=100  Half life= H= 63 years  Final amount= A= 1  Time= t years Using the half-life…

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

A:

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: 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: 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: A scientist begins with 450 grams of a radioactive substance. After 55 minutes, the sample has…

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Q: How many half lives must have passed for an isotope with a half life of 10 years to decay from 1600…

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Q: Assume a substance has a half-life of 11 years and the initial amount is 133 grams.How long will it…

A: If A0 is initial amount present and T is half -life of the substance. Then the amount of substance…

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: Given that the aspirin decays exponentially. Therefore, use the exponential model to find the…

Q: The current population of a threatened animal species is 1.7million, but it is declining with a​…

A:

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: Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000…

A: Given that the half life is 1000 years. This means 1/2 of the the original amount is left after 1000…

Q: A particular isotope has a half-life of 1 minutes.  If you start with 1 gram of this isotope, how…

A: To determine: A particular isotope has a half-life of 1 minutes.  If you start with 1 gram of this…

Q: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree…

A:

Q: If the population of a small city is 55,000. If the population grows continuously by 5​% per​ year,…

A:

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: oon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: The initial quantity of aspirin in blood stream, q0=300 milligrams Given the amount of aspirin in…

Q: Suppose you invest $2000 at a rate of 3.25% continuously, what is the worth of the investment after…

A: Given that P = $2000  rate of Interest = 3.25% continuously, we have to find what is the worth of…

Q: If an account with initial amount of 2000 dollars earns 10% interest compounded continuously, how…

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

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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: A radioactive substance is known to have a half-life of 78 years. Calculate the number of years it…

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Q: After 15 years, one fourth of the initial mass of radioactive substance has decayed. a) Find the…

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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

Q: If 250 mg of a radioactive element decays to 200 mg in 48 hours, find the half-life of the element.

A:

Q: Soon after taking an aspirin, a patient has absorbed 300 milligrams of the drug. If the amount of…

A: Let the amount of aspirin in bloodstream at time t be N(t) and initial the amount be N0. Therefore…

Q: At the beginning of an experiment, there are 100 bacteria. If the bacteria follow an exponential…

A: At the beginning of an experiment, there are 100 bacteria. If the bacteria follow an exponential…

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.