84. The number of bacteria in a container increases at the rate of R(t) bacteria per hour. If there are 1000 bacteria at time 1 = 0, which of the following expressions gives the number of bacteria in the container at time t = 3 hours? (C) f R() dt (D) 1000 + f R(1) dt (A) R(3) (B) 1000 + R(3)

Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

A:

Q: (5) Suppose 2 mg of a drug is injected into a person's bloodstream. As it metabolizes, the amount of…

A: Initially 2 mg of drug is injected and it decreases at the rate of 4% each hourWhen must the person…

Q: 2. A tank initially contains 1000 gallons of fresh water. Brine containing 3 lbs/gallon of salt…

A: The time taken for the quantity of salt to reach 100 lbs is 16.80555 minutes

Q: When time is measured in​ days, the decay constant for a particular radioactive isotope is 0.16.…

A: The equation for radioactive decay is N(t)=N0(e-λt), where N(t) is the new amount of isotope , N0is…

Q: 5. An apple pie with an initial temperature of 170 °C is removed from the oven and left to cool in a…

A:

Q: 2) A body temperature of 50 °F is placed in an oven whose temperature is kept at 150 °F. If after…

A: time required for the body to reach 100°F=?

Q: Use the graph of y = g(x) to estimate using a left, right, and midpoint Riemann sum with n = 4.

A: Given: The graph of function y = g(x), and n  = 4

Q: A 50 – gallon tank of pure water has a brine mixture with concentration of 2 pounds per gallon…

A: Form the first order differential equation then find its solution to get amount of salt at any time…

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: a new substance C is to be formed by removing two units from each of two substances whose initial…

A: 1st we will formed a differential equation for amount of C and then solve it to get actual amount of…

Q: 9. The rate at which the value, V, of a painting changest years after it is completed is given by…

A: Image is attached.

Q: Suppose x and y are functions of third variable t. In the equation x2+y²=45, what are the values of…

A: This question is related to application of derivatives.

Q: 4. Coffee at temperature 180°F is cooling in a room with constant temperature 75°F. If it takes for…

A:

Q: In a first order chemical reaction with no backorder reaction the concentration of the reactant is…

A: We solve for C(t)

Q: 3. Imagine you fill your bathtub up at a rate of 2 gallons per minute. This means that every minute…

A:

Q: John is an epidemiologist. He is tasked to determine the rate at which the total average of COVID…

A:

Q: 2. The rate at which the number of bacteria in a culture is changing (in thousands of bacteria per…

A: As per our limit we can answer only the first question. If you want other questions to be answered…

Q: Suppose that h = 2x'y, where both x and y are changing with time. At a certain instant when x = 1…

A:

Q: 2. For a substance C, the time rate of comversion is proportional to the square of the amount x of…

A:

Q: (12 Use differentials to est imate fl-2.01) it fCx): x/T-x.

A: We need to find differential estimate. NOTE- As per Bartleby's guidelines we can only solve one…

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

A:

Q: Suppose you have a 200-gallon tank full of fresh water. A drain is opened that removes 3 gal/sec…

A: Let the concentration of brine =x lb/gal Amount of salt entering in per minute = 2 gal1 min×x lb1…

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

A:

Q: When it comes to bacteria growing by binary fission, its generation time will be the time interval…

A: Given,              G=t3.3 logbB; G= generation time  t=  time interval in hours or minutes b=…

Q: Here is a new twist on the question. Suppose we want to cool our hot coffee to 100 °F as quickly as…

A: Given:T(t) = A + (To-A)e-ktA = 72°Fk = 0.125To=170°F HenceT(t) = 72 + 170-72e-0.125tT(t) = 72 +…

Q: The total cost in pesos of producing x pools of low voltage cable is given by C = 0.002 x - 05 x2 50…

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: Supposed that the yearly rate of consumption of oil (in millions of barrels) is given by C'(t) =…

A:

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: (4) The temperature at a point (x, y) is given by T(x, y) = xy + x². (a) (2, –1)? What is the rate…

A: (1) The rate of change in temperature can be determined by finding the gradient,…

Q: 3- Suppose a student carrying a flu virus returns to an isolated college campus of 8000 students. If…

A: let the number of students infected is x, therefore, the number of students not infected is 8000-x…

Q: An object is moving along a path that can be described as f(x) meters, where x is in seconds and…

A: Topic = Application of derivative

Q: 2. The liquid base of an ice cream has an initial temperature of 210°F before it is placed in a…

A: Given : The liquid base of an ice cream has an initial temperature of    To find at what time will…

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

A:

Q: Suppose the sales of potato chips generates a profit at the rate P′(t)  =  10t ln(7t) dollars per…

A:

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: Jesaki Inc will sell N units of product after spending $x thousand in advertislhg, as en by N = 74…

A: The given data is: N=74x-x2 To use differential approximation to estimate the increase in sales that…

Q: 18. Estimate the instantancous rate of change of the function f(x) = x' +4x - 11x-30 at x = 1. Round…

A: Given,  f(x)=x3+4x2-11x-30, x=1

Q: 2. It takes a car salesman 2.5 hours to drive from one city to another if he drives at a constant…

A: We know that , distance = velocity×Time

Q: quantity with an initial value of 220 grows continuously at a rate of 9.5% per hour. What is the…

A:

Q: 2. The manager of a company determines that when q hundred units of a particular commodity are…

A:

Q: The number of field mice in a certain pasture is given by the function 200 – 10t, where time t is…

A: Given: The function for the number of mice in the field = 200 - 10t To find: The differential…

Q: 13. The revenue from a manufacturing process (in millions of dollars) is projected to follow the…

A: R = 100 + 0.08t at t = 10 R = 100 + 0.8 R = 100.8 million dollars.   C = 60 + 0.2 t2 at t = 10 C =…

Q: 9) Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2x2 + 6x +…

A: Given function is as below : c(x) = 2x2+6x+12marginal cost c'(x) =ddx2x2+6x+12…

Q: 2. For a substance D, the time rate of conversion is proportional to the square root of the amount x…

A: Given For a substance D, time rate of conversion is proportional to the square root of the amount x…

Q: 2. An object with a temperature of 32°C is taken to an open field where the temperature is 42°C.…

A:

Q: With assuming ideal laboratory conditions, the number of bacteria in a culture grows by the law Q(4)…

A:

Q: 4. A tank contains 400 liters of brine. 12 liters of brine each containing 2.5 N of dissolved salt,…

A:

Q: The concentration for a first-order reaction is given by the equation: In[A] = -kt + In [A], Where:…

A: