Suppose an unknown radioactive substance produces 6400 counts per minute on a Geiger counter at a certain time, and only 200 counts per minute 12 days later. Assuming that the amount of radioactive substance is proportional to the number of counts per minute, determine the half-life of the radioactive substance. The radioactive substance has a half-life of days.

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: A radioactive substance decays at a rate proportional to the amount present, and half the original…

A: given radioactive substance that its half life is 1500 years. we have to find time after which the…

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

A:

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A: Given : S=the amount of radium you start with=250gm t=the amount of time in years=950 years  h=the…

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: 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: The radioactive isotope Carbon-14 has a half-life of 5,730 years. Given 300 grams of C-14, what is…

A: topic - exponential function

Q: suppose the half-life of caffeine in the bloodstream of a healthy adult is 6 hours. If the person…

A: Given: initial quantity of caffeine C0=200 mgt=12 hrs (11 am to 11 pm)half life t12= ln 2K…

Q: The rate growth of a population is proportional to the present population. If it is 1000 initially…

A: This question is related to the population growth, We will solve it using integration.

Q: The half-life of the radioactive element tritium is 12 years. Find its decay constant.

A: We have, the half-life of the radioactive element tritium is 12 years. As we know that, The time in…

Q: The population of a state is known to grow at a rate proportional to the number of people presently…

A: Follow the steps.

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: A certain radioactive substance decomposes at a rate proportional to the amount present. Suppose…

A: I have appended the formula used in the solution part.

Q: If the growth rate of a culture of bacteria is proportional to the number of bacteria present. After…

A:

Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is…

A: Half-life = 0.693/Decay constant(lambda)

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A:

Q: A certain radioactive substance has a half-life of 38 hours. The rate of change in the decay is…

A: In this we are going to use decay formula so I'm providing hand written solution for this

Q: For a period of time, an island's population grows at a rate proportional to its population. If the…

A: The general growth formula is given by,

Q: The half-life of Carbon-14 is 7 years. How much of an initial 131 g sample will remain after 45…

A:

Q: The rate of decomposition of radioactive radium is proportional to the amount present at any time.…

A: The rate of decomposition is proportional to y, we know that y=Cekt, where t is the time in years.…

Q: Assume that the population of a certain city increases at a rate proportional to the number of…

A: Note: There are two problems of same type. We will solve the first one for you. Kindly repost the…

Q: It is known that the population of a certain country at time t is proportional to the people living…

A: Given:- It is known that the population of a certain country at time t is proportional to the people…

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: The radioactive element Carbon-14 has a half-life of approximately 5730 years. A fossil is measure…

A: Given : Half life of carbon- 14 is 5730 years

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

A:

Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

A:

Q: Radium decomposes at a rate proportional to its present radioactive. In 100 years, 100 units of…

A:

Q: A radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium…

A:

Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A:

Q: Find the half-life (in hours) of a radioactive substance that is reduced by 10 percent in 90 hours.

A: Half-life = 0.693/(Decay constant)

Q: A sample of a radioactive substance decayed to 10% of its original amount after 30 years. What is…

A: Given After 30 years substance decayed to 10 % of its original amount

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

A:

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

A:

Q: Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount…

A: A(t)=A012thh is the half lifeA(t) is the amount after t years.A0 is the initial value.

Q: Consider 250g of iodine which decomposes at a rate proportional to the amount present. Around 150g…

A: According to the company guidelines only first three 3 subparts will be answered in case of multiple…

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A:

Q: After 25 years, 60% of a radioactive substance still remains in a 20 gram sample. What is the…

A: Half life of a radio active material is the time required to reduce the initial quantity to its…

Q: A tumor is injected with 0.7 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

A: The exponential function A = P * (1 - r)t  where A is the final amount and P is your inital amount.…

Q: Radium decomposes at a rate proportional to the amount present. If half of the original amount…

A:

Q: A radioactive substance has a half-life of 4 hours. How much of it is left after 12 hours?

A: Since, a radioactive substance has a half-life of 4 hours.Our aim is to calculate the amount of…

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

A:

Q: The half-life of radioactive radium (226Ra) is 1599 years. What percent of a present amount of…

A:

Q: Consider the constant rate of depreciation value of a certain car. You bought a car amounting to 1.5…

A:

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: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

Q: A certain radioactive substance has a half-life of 38 hour. Find how long (in hours) it takes for…

A:

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.