he drug Valium is eliminated from the bloodstream with a half-life of 36 hr. Suppose that a patient receives an initial does of 20 mg of Valium at midnight. (a) How much Valium is in the patient’s blood at noon the next day? (b) When will the Valium concentration reach 10% of its initial level?

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: Suppose $5,000 is invested at 7% intrest compounded continiously. How long will it take the…

A: The investment amount P = $ 5000. The interest rate r = 7% compounded continuously. The final amount…

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: The half-life of Radium-226 is 10 years. How much of an initial 138 g sample will remain after 49…

A:

Q: if the population of Palestine is 6 million in 2020  with a growth rate of 3%/yr when it is expected…

A: Given: The population of Palestine is 6 million in 2020  with a growth rate of 3%/yr

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

A:

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: A radioactive substance has a half-life of 64 hours. If 200 grams of the substance are initially…

A:

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

A:

Q: Radium decomposes at a rate proportional to the quantity present. If at the end of 20 years…

A: Solution

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: A certain drug is eliminated from the bloodstream with a​ half-life of 34 hours. Suppose that a…

A:

Q: Radioactive cesium-137 has a half-life of 30.17 years. How much of an initial amount of 1,000…

A: If N0 is the initial amount and t is the number of years then equation of decay  is given by…

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

A:

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 radioactive substance decays at a rate proportional to the amount present ( y(t) = yoe-rt ) If 40%…

A: let the amount of radioactive material be x, and Given that…

Q: 4.) The half-life of strontium-90 is 28 years. Find the rate of decay. How long will it take a 50 mg…

A:

Q: Radioactive radium has a half-life of 1899 years. If 20g of the substance are present initially,…

A:

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: Strontium-90 has a half-life of 29 years. If there are 400 grams of strontium initially, how much,…

A: Strontium-90 has a half-life of 29 years, there are 400 grams of strontium initially.

Q: The half-life of plutonium-241 is approximately 13 years. How much time is necessary for a sample…

A: The exponential formula for decay is given as: A=A0e-λt               ⋯2, where A is future amount,…

Q: The half-life of radium-226 is approximately 1620years.a. How much of a sample weighing 4 g will…

A: For a radioactive material, we have N(t)=N012tt1/2 Where N(t)=quantity of the material remaining.…

Q: Find the amount after 3 years if $ 1000 is invested at an intrest rate of 12% per year, compounded…

A: Given :             The amount invested is $1000.             Interest rate = 12% per year.…

Q: A tumor is injected with 0.4 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

A:

Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

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: How long will it take for 1000 to decay to 500 with a loss of 3% a year (approximate historical…

A: Given : Initial value = 1000 Final value = 500 Loss is 3% per year Apply the exponential decay…

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

A:

Q: 9. If you invest $2500 at 2.8% compounded continuously how much will you have at the end of 10…

A:

Q: Radon-222 decays at a continuous rate of 17.3% per day. How much will 250 mg of Radon-222 decay to…

A: Radon-222, a noble gas resulting from the decay of naturally occurring uranium-238, is the first…

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

A:

Q: A toxic radioactive substance in the amount of 7 miligrams per square centimeters is detected in the…

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

A:

Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

A: Given:             dAdt=k 0.043% of total amount has disintegrated :              =100-0.043%…

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

A:

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

A:

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: a) If an investment grows in value at 2.4% per year, how long will it take for its value to double?…

A:

Q: A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days, the…

A: We have to find the decay rate of the radioactive compound.

Q: 2. At what rate of interest, compounded continuously will an investment double in six years? 3.…

A: (2) given that the principle amount will gets doubled in six years if the amount is compounded…

Q: 2. A radioactive material loses 25% of its mass in 10 minutes. What is its half-life?

A: Let No be the initial mass, N be remainingmass.  Then  N= No - 25100 No = No - No4=34NoHence    t…

Q: $3,500 is invested at a rate of 6% coumpounded weekly. What is the amount at the end of 15 years?

A: Principal amount P = $3500 Rate r = 6% weekly             =( 6/52)% annually  Time t = 15 years  =…

Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: The half-life of Cobalt-60 is 14 years. How much of an initial 107 g sample will remain after 27…

A:

Q: Radon-222 has a half-life of 4.00 days. Given its mass 3.168 gram at a certain time, what was the…

A: We will find out the required solution.

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.