4. The temperature of a warm object can be found by T= A + (To – A)e“, where A is the temperature of the surroundings, To is the initial temperature of the object, t is the time in minutes since the initial temperature was measured, and k is a characteristic of the object. At what rate is a cup of tea cooling 4 minutes after its initial temperature of 78°C was taken, with a room at a temperature of 23°C, and has ak value of 0.043?

Q: 3. A plastic of warm water with a temperature of 110°F is placed inside a 0°F freezer. After 20…

A:

Q: 2. A certain radioactive material is known to decay at a rate proportional to the amount  present.…

A:

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A: Here efficiency of the workers after t hours from 9.00AM is given.  We have to find the workers…

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A: Suppose that copper is being projected to be extracted from a certain mine at a rate given by

Q: 2. A body at 100°C warms at 120ºC after 5 minutes in a surrounding at 30°C. At what time will its…

A: Given- T0=100°C,Ts=30°C ,T=120°C To Find- The time at the temperature of the body will be double.…

Q: Under certain conditions, the number of diseased cetls N(t) at time t increases at a rate N'(t) = A…

A: Rate at which number of diseased cells N(t) are increasing at time t is given by N'(t)=Aekt.…

Q: 3. The rate at which radioactive nuclei decay is proportional to the number of such nuclei that are…

A:

Q: The number of units Q of a particular commodity that will be produced with K thousand dollars of…

A:

Q: 4. It is estimated that x months from now, the population of a certain town will be changing at a…

A: First we will integrate p'(x) to find the function p(x) and then we will find the population 27 from…

Q: This question is designed to be answered with a calculator. The rate at which the value of a bank…

A: Rate at which bank account changes is- dVdt=kV Then, dVV=kdt Integrating to both sides-…

Q: 3. A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: We row that general equation for the radio active decy is M=M0e-kt            Where "M0 " is…

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A: (a)

Q: 13. Consider a prolific breed of rabbits whose birth and death rates, B and 8, are each proportional…

A:

Q: A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial…

A:

Q: Under certain conitions, the number of diseased cells N ( t ) at time t increases at a rate N ' ( t…

A:

Q: Suppose that in a certain country the life expectancy at birth of a female is changing at the rate…

A: Rate of change of life expectancy at birth of a female as a function t is given by, Here t is…

Q: 2. It is estimated that t months from now, the population of a certain town will be changing at the…

A:

Q: 1. The heat index (HI) is an estimate of the temperature felt by the human body based on the actual…

A:

Q: 17. Suppose the radius r, height h, and volume V of a cylinder are functions of time t, and further…

A: Simply write the volume of the cylinder and differentiate with respect to h.

Q: If a snowball melts so that its surface area decreases at a rate of 4 cm2/min, find the rate (in…

A: Let the diameter be D cm and radius be r cm  The surface area S of the the sphere in term of…

Q: 1. The rate at which radioactive nuclei decay is proportional to the number of such nuclei that are…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: 3. At time t, a certain radioactive material is known to decay at a rate proportional to the mass,…

A:

Q: 2. Suppose the remaining quantity, measured in grams, of a radioactive substance present after time,…

A: Given: Qt=500e-0.05t we know that at half life quantity of radioactive substance will be half of…

Q: 18. Two cars start moving from the same point. One travels south at 60 mi/h and the other travels…

A:

Q: It is estimated that x months from now, the population of a certain town will be changing at a rate…

A: This is a problem related to integration. Based on the general formula and concept we will answer…

Q: 1. a) A car is driving toward an intersection from the east at 40 mi/h, and a second car is driving…

A: Here the two cars are approaching each other at right angles with different speeds. Therefore the…

Q: A body of an unknown temperature is placed in a room which is held at a constant temperature of 30 .…

A: Given that, A body of an unknown temperature is placed in a room which is held at a constant…

Q: Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both…

A: (a)

Q: Solve parts a,b, and c.

A: Here we need to apply some basic concepts of derivatives to find the answers

Q: 2. It is estimated that t months from now, the population of a certain town will be changing at the…

A: This question is related to population growth, We will solve it using integration.

Q: Suppose the depth of water in the lake at time t is given by h(t) = 5 -1/3t What is the average…

A:

Q: While Mia is playing in a sandbox, Mike, a biochem unyor, is sitting in a lab and trying to solve a…

A: Fghh

Q: 1. A body at 50 degrees C cools inside a room with temperature of 30 degrees C. At what temperature…

A: Let's find.

Q: Suppose that the number of bacteria in a culture at time t is given by N = 5000 (25 + te ). (a) Find…

A: Given that the bacteria culture model at a time t is given as  Nt=500025+te-t20 To find the largest…

Q: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

Q: 9. Suppose an object is moving along a path described by; f(t) = t° – 6t, where f (t) is measured in…

A:

Q: a) The cost(C) in GH¢ of catering per head in a restaurant with the number (N) of people present is…

A:

Q: b. A spherical metal ball with initial temperature of 190°C is placed outside where the temperature…

A:

Q: A bacterial colony is estimated to have a population of P thousand individuals, where P(t) = 24t +…

A:

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A:

Q: It is estimated that t months from now, the population of a certain town will be changing at the…

A: This question is related to population growth, We will solve it using integration.

Q: 4. The population of a trading area is currently 100 thousand. At time t years from now population…

A:

Q: () 18 where M, is the The half-life of a radioactive element can be modelled by M= Mo initial mass…

A: The half-life formula is N=N012tt12. Here, N is the quantity remaining after time t, N0 is the…

Q: Suppose that copper is being projected to be extracted from a certain mine at a rate given by P'(t)…

A:

Q: 1) A pump is used to fill an inflatable mattress at a constant rate of 0.25 cubic feet per second.…

A:

Q: A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution…

A:

Q: 17 It is found that the bloodstream concentration, C (in ug/mL), can-be modeled by C(r) T2 + 11…

A: According to the our guidelines we are supposed to do only first three subparts. Kindly repost the…

Q: Y = 4000 ( 1- 50

A:

Q: 2- An efficiency study of the moming shift at a certain factory indicates that an average worker who…

A:

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A: Given relation is: Qt=-t3+6t2+24t a). The worker's rate of production at 11 AM: So put t=3 in given…

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.