: In a certain culture of bacteria, the rate of increase is proportional to the number present. FIND : (a) If it is found that the number doubles in 6 hrs, how many may be expected at the end of 18 hrs? (b) If there are 102 at the end of 4 hrs, and 8 ∙ 102 at the end of 8 hrs, how many were there in the beginning?

Q: Solve using Differential Equation Pure water enters the tank at the rate of 3 gal/min and brine…

A: Let y be the amount of a substance. The concentration of the substance can be modeled using the…

Q: APPLICATION OF 1st ORDER DIFFERENTIAL EQUATIONS 1. Brine containing 3 lb/gal of salt enters a large…

A:

Q: ELEMENTARY APPLICATIONS OF DIFFERENTIAL EQUATION (DILLUTE AND MIXTURE) Lake Taal has a volume of…

A:

Q: 3. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the…

A: Solve these question by differentiation method.

Q: Differential Equation A brine solution flows at a constant rate of 10 L/min into a large tank that…

A:

Q: a body at a temperature of 50°F is placed in an oven whose temperature is kept at 150°F. If after 10…

A: We can use differential equation or Newton law of cooling to solve the problem

Q: #9

A: Given:Initially water tank holds 300 gallons of water.Rate at which the pure water is pumped into…

Q: A cylindrical container, 80 cm in diameter is initially filled with water to a depth of 119.367 cm.…

A: Given that, A cylindrical container, 80 cm in diameter is initially filled with water to a depth of…

Q: Differential Equations. A 40◦F roast is cooked in a 350◦F oven. After 2 hours, the temperature of…

A: A 40◦F roast is cooked in a 350◦F oven. After 2 hours, the temperature of the roast is 125◦F. The…

Q: Elementary Applications of Differential Equations 4. A tank initially holds 100 gallons of salt…

A: Here is the Answer and Explanation

Q: (12>Application of Differential Equation of Order One<) Moonlight at High Noon. The fact that…

A: 100-15=85% of the intensity of brightness of light is at the depth 25 ft.

Q: Give two examples of your own for order and degree of a differential equation

A:

Q: A lake holds a population of 600,000 trout. The natural growth rate of the trout population is 5%.…

A: Given : A lake holds a population of 600,000 trouts. The natural growth rate of the trout population…

Q: Newton's Law of cooling, which also can be applied to heating problems, states that "the time rate e…

A:

Q: DIFFERENTIAL EQUATION: A year-end party is being held in a room that contains 30 m3 of air which is…

A:

Q: . Applications of Differential Equation 1. The population of a town grows at the rate proportional…

A:

Q: A body cools in air of constant temperature of 20 ℃ . Five minutes after the body began to cool ,…

A:

Q: The population of a certain barangay is known to increase at a rate proportional to the number of…

A:

Q: (Differential Equations) A thermometer is taken from an inside room to the outside, where the air…

A: It is given that A thermometer is taken from an inside room to the outside, where the air…

Q: Newton's Law of Cooling states that the rate at which an object cools is proportional to the…

A: Given:  An object is taken from an oven at 309°F and left to cool in a room at 75°F, its temperature…

Q: n to grow at a rate proportional to the amount present. After 60 minutes, 5,000 strands of the…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Particle A decays with a decay constant 1 to become particle B, which will decay into a C particle…

A: Solve the first differential equation:

Q: A vat with 500 gallons of beer contains 4 % alcohol ( by volume ). Beer with 7% alcohol is pumped…

A:

Q: The differential equation of the family of straight lines whose sum of slope and x-intercept is…

A:

Q: wasp population has a 10 percent birth rate and a 7 percent death rate. Every year people swat an…

A: Given query is to find the differential equation for the problem.

Q: Differential Equations: A large tank initially contains 100 liters of brine in which there is…

A:

Q: Newton's Law of Cooling tells us that the rate of change of the temperature of an object is…

A:

Q: A large tank initially contains 500L of brine in which 100g of salt is dissolved. Brine containing…

A: This question is related to differrential equations, We will solve it using given information.

Q: Application of Differential Equation: A 0.8-H inductor is connected in series with a 7-ohm resistor.…

A:

Q: A solution containing 2lb of salt per gal starts to flow into a tank of 50 gal of pure water at a…

A: Given that, A solution containing 2lb of salt per gal starts to flow into a tank of 50 gal of pure…

Q: (Differential Equations) A homicide victim is found at 6:00 PM in an office building that is…

A: Given that, Temperature at the time of death, is assumed to be normal. 98.4°F Homicide victim was…

Q: A rumor begins to spread in a population of 10,000 inhabitants thanks to a member of the population…

A:

Q: Draw the diagram and solve of the following statements:   4. It was 3am when a computer bug…

A: Given: It was 3am when a computer bug infected the Google server which has 1500 modules. At 3:15am,…

Q: Differential Equations: Solve for Yp: 4.) 18D³-15D²-85D+100 = 0

A: Given differential equation is 18D³-15D²-85D+100 = 0

Q: Newton's law of cooling states that the rate at which temperature T of a body falls is proportional…

A:

Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the rate of increase of…

A:

Q: Solve using differential equation  A certain chemical dissolves in water at a rate proportional to…

A: Please check step 2 for the solution.

Q: 3. A tank is filled with 8 gal of brine in which 2 lb of salt is dissolved. Brine having 3 lb of…

A: Given,  A tank is filled with 8 gal of brine in which 2 lb of salt is dissolved. Brine having 3 lb…

Q: A small metal bar, whose initial temperature was 20°C, is dropped into a large tank of boiling…

A: First we formulate differential equation by given condition rate of increase rate of temperature .…

Q: A thermometer is removed from a room where the air temperature is 70 degree F to the outside, where…

A: A thermometer is removed from a room where the air temperature is 70 degrees F to the outside, where…

Q: (3y²-x² ()y' -=0 ;when x = 1, y = 1 2y4

A:

Q: ELEMENTARY APPLICATIONS OF DIFFERENTIAL EQUATIONS (GROWTH AND DECAY METHOD) Jun has decided to save…

A: Introduction: The exponential growth and decay model is useful in calculating the amount related to…

Q: A tank contains 1000 kg of a 10% salt solution. A stream containing salt at 20% concentration enters…

A:

Q: 8. y = (C1 + C2x)e* + c3e2x %3|

A: The solution of the problem is given in the next step.

Q: Suppose it was known that the cells of a given bacterial culture divide every 3.5 hours, if there…

A:

Q: DIFFERENTIAL EQUATION Solve the IVP, where x = f(t) and x" - 4x = 0 subject to the conditions that…

A: To solve given initial value problem first we write the characteristic equation of given…

Q: A dirty lake was contaminated by a toxic substance. The lake has a volume of 100,000 liters of water…

A: This question is related to the differential equations, We will solve it using given information.

Q: A tank originally contains 120 litre of brine with a salt concentration of 4 gram of salt per litre.…

A: Given that, A tank originally contains 120 litre of brine with a salt concentration of 4 gram of…

Q: Elementary Applications of Differential Equations 2. The population of a country doubles in 50…

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.