A tank with a capacity of 800 L is full of a mixture of water and chlorine with a concentration of 0.025 g of chlorine per liter. In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 8 L/s. The mixture is kept stirred and is pumped out at a rate of 20 L/s. Find the amount of chlorine in the tank as a function of time. (Let y be the amount of chlorine in grams andt be the time in seconds.)

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: a: it doubles in every 30 minute and initial population = 10 then we can write the function as:…

Q: If an archer shoots an arrow straight upward with an initial velocity of 160ft/sec from a height of…

A: If the arrow reaches the ground then h(t)=0…

Q: The function f(x) = x3 describes the volume of a cube, f(x), in cubic inches, whose length, width,…

A: Given function is fx=x3

Q: If the total population of deer on an island as a function of years is 1000-900e-0.02t  then the…

A: For a positive number n, the logarithm of n is the power to which some number b must be raised to…

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: The Loth Cat population grows at a constant relative growth rate. If the population is 400 after 2…

A: Let the constant relative growth rate be 'r' and the time in years be 't'. Let the population at any…

Q: the number of bacteria in a culture was initially 8,000 and the number grew to 12,000 in 6 hours.…

A:

Q: A population of bacteria is initially 8000. After three hours the population is 4000. If this rate…

A: Given,          A population of bacteria is initially 8000. afters three hours the population is…

Q: Suppose that a room containing 1500 cubic feet of air is originally free of carbon monoxide.…

A:

Q: Sketch the graph of a function f such that f′ > 0 for all x and the rate of change of the…

A: Given A function f with f’>0 and rate of change is decreasing.

Q: itially contained 8000 L of pure water. The resulting concentration of the solution in the tank can…

A: In the given question, concept of limit on maximum concentration is applied and asymptote is clearly…

Q: If the population (in millions) of a country as a function of time (in years) is P(t) = 10 · 2kt,…

A:

Q: The half-life of a certain radioactive substance is 5 days. There are 28.4 g present initially. a.)…

A:

Q: find the net change in g between x=0 and x=7

A: Here we have to find the net change.

Q: For oits economy class accomodation from Cebu City to Manila, a shipping line gives free passagw to…

A: Given, For oits economy class accommodation from Cebu City to Manila, a shipping line gives free…

Q: A company has determined that its price-demand function for its sale of its product is given by…

A:

Q: Consider the following situation. A tank contains 2500 L of pure water, with 15 kg of salt dissolved…

A: Let consider that function s(t) is kgs of salt in the tank at time t minutesAs we know thats'(t)=The…

Q: If f and g are functions of time, and at time t = 2, f equals 3 and is rising at a rate of 5 units…

A:

Q: A long distance company charges a monthly fee of $4.95 and $0.02 per minute. Let f(x) be the monthly…

A: Solution:

Q: The function f(x) = x2 describes the area of a square, f(x), in square inches, whose sides each…

A: Given function fx=x2 to find rate of change of area.

Q: Find the instantaneous rate of change of the function at the specified value of x. f(x)=(x−3)/(x+5)…

A: Given data:     The given function is: f(x)=(x-3)/(x-5).   The expression for the rate change of the…

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = 2x² ,…

A:

Q: If f and g are functions of time, and at time t = 2, f equals 2 and is rising at a rate of 3 units…

A:

Q: The following table gives for a certain man his height H= H(t) in inches at age t in years A- use…

A: From the table, we have (0, 21.5) and (5, 42.5), Now find the slope passing through two points…

Q: pressure

A:

Q: Suppose we have a tank that contain 10 litres of water and 50 g of salt. The salt solution is…

A: given , tank that contain 10liters of water and 50 gram of salt .  so , initial concentration =>…

Q: A commuter drove to work a distance of 20 miles and then returned again on the same route. The…

A: Let x be the average velocity on the outgoing trip.

Q: A warm can of soda is placed in a cold refrigerator. Sketch the graph of the temperature of the soda…

A: The rate of cooling of an object is governed by Newton’s law of cooling. It says that the rate of…

Q: Suppose that a liquid carries a drug with concentration 0.1 g/cc into a 400-cc organ at a rate of 5…

A:

Q: The number of daily users for Japan’s Line messaging service (in millions) can be approximated by…

A: The approximating function that represents the given scenario is: g(x)=53.1+63.1 ln(x) where x…

Q: The demand for a natural resource t years from now will be increasing at a rate of te0.0017 million…

A:

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

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: From a 27-cm by 27-cm piece of cardboard, square cormers are cut out so that the sides can be folded…

A:

Q: (a) A kitchen sink has a volume of 15 L. If the drain is closed and the sink is initially empty,…

A:

Q: ) Greenland had a population of 55000 in 1980 and a population of 78000 in 1990. Assume that the…

A:

Q: The growth rate of Escherichia coli, a common bacterium found in the human intestine, is…

A: Given The number of cells doubles every 30 minutes. A) Initial Population =1000 B) Initial…

Q: A mouse wheel is 16 cm im diameter and the base of the wheel is 2 cm off i ground. If the hamster…

A:

Q: A bucket that weighs 3 lb and a rope of negligible weight are used to draw water from a well thatís…

A: weight of bucket=3lb weight of water at starting=37lb deepness of the well =60 feet bucket lifts at…

Q: We can use a linear function to describe air leaking from a balloon, but this is not, in fact, an…

A:

Q: According to the U.S. Census Bureau, in 2011, the median (middle of the range) annual income of a…

A: Since multiple subparts are posted, we will solve the first three subparts only. To get the…

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: To determine a function P(t) that models the number of bacteria after t minutes.

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

A:

Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=700e0.24t…

A:

Q: Q2/ A tank contains initially (150) liter of brine in which (60)N of salt is dissolved starting at…

A: The amount of salt in the tank at the end of 5 min is 111.38779 N

Q: The size P of a small herbivore population at time t​ (in years) obeys the function P(t)=1000e0.2t…

A:

Q: A culture contains 2000 bacteria initially and doubles every 40 minutes. Assuming that the rate of…

A:

Q: If f and g are functions of time, and at time t = 3, f equals 9 and is rising at a rate of 4 units…

A: Given,            If f and g are functions of time. At t = 3 , f equals to 9 and is rising at rate…

Q: Express the area A of a right triangle as a function of the height h if the base of the triangle is…

A:

Q: The crime rate of a certain city is decreasing by exactly 3%each year. Let t=0 correspond to the…

A: The function that represents the continuous decrease in number of crimes is given by:

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

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.