A CERTAIN RADIOACTIVE MATERIAL IS KNOWN TO DECAY AT A RATE PROPORTIONAL TO THE AMOUNT PRESENT. IF AFTER ONE HOUR IT IS OBSERVED THAT 10% OF THE MATERIAL HA DECAYED, FIND (a) AN EXPRESSION OF THE MATERIAL REMAINING AT ANY TIME (b) FIND THE HALF-LIFE MATERIAL.

Q: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

A: Population decay

Q: A bank pays interest at a rate of 5%. What is the yearly multiplier if interest is compounded (a)…

A:

Q: Of an initial amount of 6000 g of lead-210, how much will remain in 110 years? Lead-210 decays at a…

A:

Q: Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100 mg…

A:

Q: 2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately…

A: Let  at time t the amount of plutonium is  A(t)

Q: 6. The radioactive isotope of lead, PB-209, decays at a rate proportional to the amount present at…

A: Let's find time to take 90% of the lead to decay.

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: ind the half-life of a radioact

A: Given that: Rate = 12 %

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

A:

Q: The decay constant for the radioactive element strontium 90 is l = .0244, where time is measured in…

A: Definition used -                            Decay equation -…

Q: A quantity with an initial value of 840 decays continuisly at a rate of 5% per day. What is the…

A:

Q: Suppose a sample of a certain substance decayed to 65.8% of its original amount after 300 days. (Ro…

A: Given that the substance decayed to 65.8% of its original amount after 300 days. (a) To determine…

Q: If the present value of $1000 to be received in 5 years is $559.90, what rate of interest,…

A:

Q: A culture of bacteria obeys the law of natural exponential growth. If 140,000 bacteria are present…

A: We can make it easier for you.

Q: of a radiooctive substonce decayed to 93.5% of its original sample amount after oyear What is the…

A: we need find half life substance k=? and t=?

Q: sample of a radioactive isotope had an initial mass of 390 mg in the year 2007 and decays…

A:

Q: Of an initial amount of 9000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A: Apply the formula  P(t)=Po(1-r)t where, Po is the initial quantity r is the rate and t is the time.…

Q: 2. Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

A:

Q: What is the half-life of a radioactive substance if it takes 5 years for one-third of the material…

A: We have to find half life period

Q: The population of minnows in the lagoon is 5,400, but the population will decay exponentially. If…

A: The formula for the exponential decay model is, y=C1-rt Here, y is the final amount C is the initial…

Q: A certain substance decays so that each year 92% of the previous year's material is still present.…

A: A substance decay such that each year 92% of the previous year's material still remains. So, 8% of…

Q: A scientist wants to determine the halflife of a certain radioactive substance. She determines that…

A: The half life function is given by: N(t)=N0(0.5)t/t1/2 where N(t) is the final amount in milligrams…

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: It is found that 0.5% of radium disappears in 12 years, a.) What percent will disappear in 100…

A: We have to find the half life of the radium

Q: The decay constant for carbon-14 is 0.00012, with time measured in years. A piece of papyrus…

A: Decay of any radio active substance follow first kinetics and the equation of first order kinetics…

Q: Suppose a sample of a certain substance decayed to 73.6% of its original amount after 300 days.…

A:

Q: A quantity with an initial value of 8200 grows continuously at a rate of o.55% per decade. What is…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present

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: A radioactive substance has a half life of 175 years. Find the decay constant, r, for this…

A: A radioactive substance has a half life of 175 years

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 190 years? Lead-210 decays at a…

A: Here initial amount A0=4000g Decaying rate λ= 3.15% = 0.0315 Let amount remains in 190 years= A(t)

Q: Suppose that the half-life of a substance is 250 years. If there were initially 100 g of the…

A:

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: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

A:

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

A:

Q: An Asian country had a population of about 0.90 Billion people in 1995 and a growth rate of 1.3% per…

A: *** This is the problem related to financial mathematics and we are advanced math expert and have…

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

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: A quantity with an initial value of 870 decays continously at a rate of 0.75% per day. What is the…

A:

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 130 years? Lead-210 decays at a…

A: Find much much will remain

Q: An environmental study of a certain community suggests that t years from now the level of carbon…

A: Let's find.

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: Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

A:

Q: A species is considered to be endangered if it is expected to be extinct within 20 years. A…

A:

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: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

Q: If the half-life of a radioactive substance is 7,300 years, then at what rate is it decaying? (Hint:…

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.