The concentration of a drug in an organ at any time t (in seconds) is given by x(t) = 0.08 + 0.12(1 – e-0.02:) where x(t) us measured in grams per cubic centimeter. What is the initial concentration of the drug in the organ? What is the concentration of the drug in the organ after 20 seconds? What will be the concentration of the drug in the organ in the long run? (Hint: Evaluate lim x(t).) 2.

Q: A radioactive substance decays according to the equation N = 105 e SIA where N is the number of…

A:

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

A: Here, initial mass =50 mg rate is proportional to the amount.m=50e-0.053t dmdtαm

Q: A bacterial population is 7000 at time t = 0, and its rate of growth is 1,000 · 4t bacteria per hour…

A: It is given that at t=0 bacteria population is 7000   The growth rate is 1000*4t

Q: What is the amount of salt in the tank at time t = 0?

A:

Q: When air expands adiabatically (without gaining or losing heat), its pre and volume V are related by…

A: For decreasing rate apply negative sign

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: After t hours, the percentage of alcohol in the blood decays according to the differential equation…

A: After time t=9.555 hours....they can legally drive...for detail solution...go through the 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: Given that the size of the tank is 200 gallon. Half of it is full, that means 200/2=100 gallon is…

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

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

A:

Q: The isotope thorium-234 has a half-life of 24.5 days. (a) What is the differential equation…

A:

Q: The population of a bacteria culture grows at a rate of P = 100(2)n, where P is the population and n…

A:

Q: The yearly rate of consumption of natural gas (trillions of cubic feet) for a certain city is…

A:

Q: A sample of 800 g of an isotope decays to another isotope according to the function A(t)= 800 e…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P C where C is a…

A:

Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

A: This question is about application of differential equation

Q: Most savings banks advertise that they compound interest continuously, meaning that the amount S(t)…

A:

Q: A chemical flows into a storage tank at a rate of (180 + 3t) liters per minute, where t is the time…

A:

Q: The amount of a radioactive isotope present at time t is given by A(t)=300e−0.0283t ​grams, where t…

A:

Q: For an ideal gas, the pressure is related to temperature and volume by the formula 8.31T . If your…

A:

Q: The amount remaining of a 162 mL sample of a liquid substance, y (in mg) after x hours is modeled by…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given : A town predicts that its public school population will decrease at the rate of

Q: The concentration of an antihista-mine in the bloodstream of a healthy adult is modeled by C = 12.5…

A: 6 hour period means from t=0 to t=6That is from start of the medication  to 6 hours after medication…

Q: A radioactive substance decays at a rate proportional to the amount present. If the initial mass of…

A:

Q: As a salt dissolves in methanol, the number x(t) of grams of the salt in a solution after t seconds…

A:

Q: Assume that the rate of evaporation for water is proportional to the initial amount of water in a…

A: Here, given that rate of change of evaporation is proportional to the initial amount of water.…

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: 3. When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, C, in…

A: Given that The concentration of pollutant C in the pond at t hours is modelled by

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

A: Let,Decay rate = r = -dAdt                        negative because it's decaying/decreasingwhere, r…

Q: The rate at which radioactive nuclei decays is proportional to the number of such nuclei that are…

A: Given Half of the original number of radioactivenuclei have undergone disintegration in a period of…

Q: The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential…

A:

Q: A water tank has 142 gallons of water, At first, in t=0, a solution with 1/6 lb/gal of a chemical…

A: it is mixing problem we use linear differential equation to solve this question.

Q: The proportion of people in a community infected with a virus that stays active for two weeks is x…

A: The complete solutions are given below

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: The population of two different species are given by P1 P1 = 3 ln(t) + 10 || and P2. , where t is…

A: The population of two different species are given by P1=3lnt+10 And P2=6lnt+2 Where, t measured in…

Q: 6. The mass of a cube in grams is M = x³ + 0.1x*, where x is the length of one side in centimeters.…

A: Explained below

Q: When sugar is dissolved in water, the amount A that re- mains undissolved after t minutes satisfies…

A:

Q: Suppose that electricity is draining from a capacitor at a rate that is proportional to the voltage…

A:

Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

A:

Q: The annual world consumption of silver is predicted to be 22.3e0.0ir since 2014. Find a formula for…

A:

Q: 4) For an ideal gas, the pressure is related to temperature and volume by the formula 8.317 P = If…

A:

Q: Water flows from the bottom of a storage tank at a rate of r(t) = 4(50 − t)e −0.05t liters per…

A: Given:  rt=450-te-0.05t    , 0≤t≤50    1 We need to find the amount of water that flows from the…

Q: The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential…

A:

Q: Consider a tank that initially contains 100 gallons of a solution in which 50 pounds of salt are…

A: Here I am attaching image so that you understand each and every step.

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

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

Q: Blood carries a drug into an organ at a rate of 3 cm3/sec and leaves at the same rate. The organ has…

A: Exponential growth/decay is given by dxdy=rici-r0vx here, ri=3= rate of drug entering. and r0=3=…

Q: A pitcher of buttermilk initially at 27°C is to be cooled by settling in on a place where the…

A: At time t=0 minutes, temperature of buttermilk = 270C   At time t=20 minutes, temperature of…

Q: 6. A certain radioactive material has a half-life of 100 days. If the amount of material present, x,…

A:

Q: Early one morning it began to snow at a constant rate. At 7 A.M. a snowplow set off to clear a road.…

A:

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.