A tank contains 240 liters of water in which 30g of salt are dissolved. Salt water with a concentration of 2gr / l is pumped into the tank at a speed of 4 l / min. The well mixed solution drains at the same rate. Find the function A (t) that determines the amount of salt in the tank at time t. (Remember that the rate at which the amount of salt changes is equal to the rate at which the salt enters minus the rate at which it exits)

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Given that ,    Ecologist estimate that, when the population of a certain city is x thousand…

Q: We found that salt is added to the tank at a constant rate and it is removed from the tank at a rate…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 300-cc organ at a rate of 5…

A: Given: the concentration of the drug carried by  the liquid=0.1g/cc liquid enters and leaves the…

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: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: When polluted water begins to flow into an unpolluted pond, the concentration of pollutant, c, in…

A:

Q: Consider the population of fish in a lake, and that people commonly fish in this lake. At a given…

A: The differential equation given is as follows:…

Q: The population of the city of Bingville increases at a rate proportional to the numbers of its…

A: Let x0 is the number of inhabitants of Bingville at time t = 0 and x is the number of…

Q: A company estimates that its revenue grows continuously at a rate given by R'(t)= 2e^2t, where t is…

A: By Using simple integration

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

A: Note: Since the image contains multiple questions, as per the answering guidelines we are to solve…

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: To find the rate of change of the carbon monoxide levels per population when t=2

Q: A population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day (t in days). Find…

A: Given that, The population of insects increases at a rate of 200 + 10t + 0.25t2 insects per day. At…

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

A:

Q: 5. If the population P of bacteria (in units of 1000) is declining because of a toxin, its rate of…

A:

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rqa', in millirems per hour.…

A: Given: The rate of decay of a substance is given by, , where is a initial amount of substance.

Q: A population of mites growsat a rate proportional to the number present, y. If the growthconstant is…

A: Assume population at time t is p Let f(t)=population at time t=p

Q: The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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 population of bacteria can be modeled by the function f(t)=1000(0.98)t where t represents the time…

A:

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5/9x² –…

A:

Q: at the rate of r (t) = 3t liters per minute, where t is the time in Which of the following defines a…

A:

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: It has been estimated that the total production of oil from a certain oil well is given by T(t) =…

A:

Q: A certain population of bacteria is known to grow at a rate proportional to the amount present in a…

A:

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

A:

Q: A culture initially has No number of bacteria. At t =1hours the number of bacteria is measured to be…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

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: The amount of radio active material present at time t is given by A=Aoe*t, where Ao is the initial…

A: As many Questions are given , I will solve only one: Let A0 be the initial amount. Given that a…

Q: 1.A culture has y,number of bacteria. At time t=2 hours, the number of bacteria is measured to be…

A: Given, Initial number of bacteria is y0. also, given at time t=2 hours, the number of bacteria is…

Q: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: A pump allows water to flow into a pool at the rate of r (t) = 2t liters per minute, where t is the…

A:

Q: A group of survivors on a supply run has returned to their base camp with a population of 2000. Two…

A: Given:  y       = present number of infected people 2000 = total population  y'(t)  = rate of spread…

Q: A population of insects increases at a rate of 20010t 0.25t2 insects per day 3. (t in day units).…

A: It is given that initially there are 35 insects at t = 0. So, I (0) = 35.

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: The rate of increase in the number N of bacteria in a certain culture is given by dN = 0.15N where t…

A:

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A:

Q: A certain radioactive substance is decaying so that at time t, measured in years, the amount of the…

A:

Q: A radioactive substance is decaying at a rate represented by y = h(t) = Rọa“, in millirems per hour.…

A:

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

Q: Estimate the instantaneous rate of change of the function f(x)=2x^2−1 at x=1 using the average rate…

A: The given function is,

Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: Given that, The half-life of a radioactive material whose rate of disintegration is proportional to…

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

A: In mathematics, two varying quantities are said to be in a relation of proportionality,…

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

A: Image is attached with detailed solution.

Q: Suppose that the fish population P(t) in a lake is attacked by a disease at time t = 0, with the…

A:

Q: Suppose a pollutant is seeping into the ground near a dump site at the rate of 2800 f(t) : (æ +…

A:

Q: Suppose the average daily metabolic rate for certain types of animals can be expressed as a function…

A:

Q: Find a formula for the average rate of change of f (x) = x^3 over [2, x] and use it to estimate the…

A: We use the average rate of change formula

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.