Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has a liquid volume of 125 cm3. If the concentration of the drug in the blood entering the organ is 0.2g/cm3, what is the concentration of the drug in the organ at time t if there was no trace of the drug initially? When will the concentration of the drug in the organ reach 0.1 g/cm3?

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

A:

Q: A container initially contains 15 L of water in which there is 30 g of salt dissolved. A solution…

A:

Q: A 200-gal tank is half full of distilled water. At time t=0, a solution containing 0.5 Ib/gal of…

A:

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Given by If Palladium has a half-life of of 4 days then the model is: A = A0(1/2)(t/4) We are given…

Q: A 40 gal tank initially contains 11 gal of fresh water. At t = 0, a brine solution containing 1.2 lb…

A: Given: The initial volume of water v(0)=11 gallons The initial amount of salt s(0)=1.2 lb Since rate…

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

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: To solve the following problem and find the amount of water left at 6:10pm.

Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

Q: In some chemical reactions, the rate at which the amount of a substance changes with time is…

A:

Q: A tank contains 200 gallons of fresh water. Brine containing 2 lbs/gal of salt enters the tank at 4…

A:

Q: A tank initially contains 200 L of fresh water. Brine containing 2.5 N/L of dissolved salt runs into…

A: Let "s" represents the quantity of salt in the tank. dSdt=(8×2.5)-8S200dSdt+0.04S=20   and S(0)=0…

Q: A freshly brewed cup of coffee has temperature 95°C in a  20°C room. When its temperature is 70°C,…

A: Given that, Initial temperature of coffee is T0=95°C, surrounding temperature is Ts=20°C. Also,…

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A:

Q: Initially a tank holds 100 gal of a brine solution containing 4 lb of salt. At t = 0, brine…

A: We will find out the required time.

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Given, the half-life palladium-100 is 4 days. Here, we use the radioactive decay model, given as…

Q: A sewage disposal plant has a big concrete holding tank of 100,000-gal capacity. It is % full of…

A: Let M(t) be the mass of the organic material in the tank at time t and Mt=CtVt, where C(t) and V(t)…

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A:

Q: A 15-foot ladder is leaning against a wall. If we pull the ladder away from the wall at a rate of…

A:

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given , half-life of Palladium-100 is 4 days        t1/2=4 days Let N(t) be the quatity after t days…

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Given :Half life of Palladium-100= 4 days

Q: A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt enters at 2…

A: Given that, A tank contains 80 galloons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: A 200g-tank holds 100 gallons of fresh water upon first. At t = 0, a 5 gal/min salt solution…

A: Given initial quantity of freshwater in the 200-gallon tank = 100 gallons At t=0, salt solution is…

Q: A tank has 72 gallons of water. Brine solution with 2lbs of salt per gallon of solution enters at a…

A: here we can use differential equation to solve this question.

Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Given : The half life of Palladium-100 is 4 days and after 24 days a sample of Palladium-100 has…

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

A: Let us assume that the rate of change of the amount of material is proportional to the amount of…

Q: A yeast grows at a rate proportional to its present size. If the original amount doubles in two…

A: Let v(t) be size of yeast at t time Therefore, ds/dt  ∝ s(t) ds/dt  = ks   [k is proportionality…

Q: A tank contains 1,000 gal of brine in which 500 lb of salt are dissolved. Fresh water runs into the…

A: Form the first order differential equation and solve using separation of variables.

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A:

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 3 ft/s, how…

A:

Q: air containing 30% oxygen passes slowly into a 3 gallon flask initially filled with pure oxygen and…

A:

Q: If 150 g of copper at initial temperature of 50 °C gains 6930 J of heat when it is cooled to 170°C.…

A:

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A: Consider the decay of Palladium-100, The half life of Palladium-100 = 4 days and after 24 days…

Q: A tank contains 5000 liters (L) of a solution consisting of 182 kg of salt dissolved in water. Pure…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

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Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A: Topic-basic maths

Q: D. A ladder 10 feet long rests against a vertical wall. If the top of the ladder slides down at a…

A: Make a diagram according to the situation.

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: Topic:- function

Q: After a foreign substance is introduced into the blood, the rate at which antibodies are made is…

A: Please see the below picture for detailed solution.

Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

A:

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A:

Q: The half-life of Palladium-100 is 4 days. After 24 days a sample of Palladium-100 has been reduced…

A:

Q: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr to a patient…

A: Given that: A 150 mg per L solution of drug is administered intravenously at a rate of 30 mL per hr…

Q: A tank contains 1000 liters (L) of a solution consisting of 195 kg of salt dissolved in water. Pure…

A: Solution is given below:

Q: A 50L tank initially contains 5L of brine solution where 3kg of salt have been dissolved. At t = 0,…

A: According to the given information,

Q: A 60-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution containing 1 Ib…

A:

Q: The half-life of Palladium-100 is 4 days. After 20 days a sample of Palladium-100 has been reduced…

A: To find the initial mass of the sample.

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.