The automobile assembly plant you manage has a Cobb-Douglas production function given by P = 30x^0.6y^0.4 where P is the number of automobiles it produces per year, x is the number of employees, and y is the daily operating budget(in dollars). You maintain a production level of 800 automobiles per year. If you currently employ 120 workers and are hiring new workers at a rate of 20 per year, how fast is your daily operating budget changing?

Q: Suppose the edges of a cube are increasing at a constant rate of 8 m/hr. Then, the volume of the…

A:

Q: Suppose that the revenue from selling x washingmachines isr(x) = 20,000(1 - 1/x)dollars. Find the…

A: To find the marginal revenue we find dr/dx

Q: 3. A manufacturer determines that when x thousand units of a particular commodity are produced, the…

A: Given that: Profit function: P(x)=-400x2+6800x-12000

Q: A point is moving on the graph of y³ = x². When the point is at (-512, 64), its y coordinate is…

A: Given, A point is moving on the graph of  y3 = x2. When the point is at -512, 64, its y coordinate…

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A: Given query is to find the rate of change of area.

Q: The volume of a cube is decreasing at a rate of 24 cubic inches per minute. At the instant when an…

A: Given that  The volume of a cube is decreasing at a rate of 24 cubic inches per minute.…

Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

A: topic- application of derivatives

Q: Find the present value of a continuous stream of income over 3 years if the rate of income is…

A: Given the rate of income , ft=80e-0.08t Number of yearsT=3 Interest rater=11% The present value can…

Q: You have a large metal box filled with honey, where the width is 14 cm, the length is half its size,…

A: For the metal box, it is given that width is b=14 cm, Length is half of width, l=7 cm,  Volume is…

Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

A:

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: Suppose the edges of a cube are increasing at a constant rate of 11 m/hr. Then, the volume of the…

A: Let the side of the cube = x Edges of the cube increasing rate dx/dt = 11 m/hr

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A: Rate of change

Q: The worst ecological disaster in U.S. history began on April 20, 2010, and was caused by an…

A: bn=2.520n & rn=441,000n a). an=bn-rn=2.520n-441,000n=-4,40,997.48n

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 30x + 0.9x2 −…

A: To calculate the marginal revenue by differentiating the revenue function.

Q: A company estimates that the daily cost (in dollars) of producing x chocolate bars is given by C(x)…

A: Given that  C(x) = 930 + 0.03x + 0.0004x2

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.8x2 -…

A: The revenue (in dollars) from the sale of a product is given by, R=60x+0.8x2-0.003x3, where x is the…

Q: A rectangle is growing in such a way that when its length is 5 ft and its width is 2 ft, the length…

A: When length is:= 5 ft; When width is:= 2 ft; Rate of increasing length= 3 ft/s; Rate of increasing…

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

A:

Q: A semi-circular pool with a diameter of 25ft and a depth of 7ft has a small leak at the bottom. The…

A: Ok, assume pool to be full with water initially,    So, initial water level = 7 ft. = 7*12 inches…

Q: Suppose the amount of oil pumped from one ofthe canyon wells in Whittier, California, decreases at…

A: We know that general exponential function is  y=y0e-kt California, decreases at the continuous rate…

Q: Suppose a product has a daily marginal revenue of 46 dollars per unit, and a daily marginal cost of…

A: Given,  Marginal Cost, MC = 30 + 1/2x marginal Revenue, MR = $46 Daily Fixed Cost = $200

Q: Suppose 225 trout are seeded into a lake. Absent constraint, their population will grow by 60% a…

A: Since the growth rate is given in terms of percentage for first of all we will convert into decimal…

Q: A certain bacteria culture grows at a rate proportional to its size. If 10,000 bacteria grow at the…

A: Given: A certain bacteria culture grows at a rate proportional to its size.

Q: Determine the growth constant of a population that is growing at a rate proportional to its size,…

A: Consider the population size is given as P(t). The expression for the exponential growth rate is…

Q: Suppose 175 trout are seeded into a lake. Absent constraint, their population will grow by 60% a…

A: Recall: Logistic growth model   P(t)=m1+m-PPe-ktWe have, P=175, m=2000, k=60%=0.60, t=5 years

Q: A population of 200 rodents is growing at a rate of 5% per month. What equation model can represent…

A: The exponential growth or decay is modelled using the equation, f(t)=a(1±r)t, where a is the initial…

Q: A manufacturer of aluminum doors currently is able to sell 500 doors per week at a price of $75…

A:

Q: Assume that it costs Sony approximately C(x)=800,000+340x+0.0005x2 to manufacture x PlayStation 4's…

A: We have given the cost function C(x) = 800,000 + 340x + 0.0005x2

Q: Explain a general mathematical modeling to growth of Human population. And what will be the Iraq…

A:

Q: An engine health monitoring system consists of a primary unit and a standby unit. The MTTF of the…

A:

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells. What…

A:

Q: Suppose that the marginal revenue for a company manufacturing coffee machines is given by 100–0.5x…

A:

Q: To facilitate rapid delivery, Samurai Van Logistic Company requires that all baggage must be in…

A:

Q: city of half a million, there are initially 400 cases of a particularly virulent strain of flu. The…

A:

Q: A piece of wire of length 12 cm was cut into two pieces. The first was folded to form an equilateral…

A:

Q: Because of the popularity and power of smartphones, demand for wireless communication is growing…

A: Given:

Q: If in the year 2000 there were 1.26 million metric tons of beef produced and demand is growing at a…

A:

Q: Suppose 200 trout are seeded into a lake. Absent constraint, their population will grow by 70% a…

A: Given problem:- Suppose 200 trout are seeded into a lake. Absent constraint, their population will…

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 30x + 0.8x2 −…

A:

Q: The length of a rectangle is decreasing at the rate of 5 cm/s and its width is increasing at the…

A: Area of a rectangle = length× width Rate of change with respect to time is D/Dt

Q: A bacteria grows proportional to the square root of its current population. Starting at an initial…

A:

Q: The polluted water from Pond 1 drains into Pond 2 at 8 gallons per minute. Pond 1 initially contains…

A:

Q: he surface area of a cube is increasing at a rate of 122.2 cm2/s. At what rate is the side length of…

A:

Q: Assume that Laguna Lake has a volume of 480km^3 and that its rate of inflow (from Lake Huron) and…

A:

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 20x + 0.5x² -…

A: Given: Revenue function from the sale of a product is given by: ⇒R=20x+0.5x2-0.002x3

Q: Suppose that the marginal revenue for a company manufacturing coffee machines is given by 100−0.5x…

A:

Q: A rectangle’s length is growing at 3 inches per second, while its width is shrinking at 5 inches per…

A:

Q: The length of the rectangle is increasing at a rate of 5 centimeters per second, and its width is…

A:

Q: Suppose to tal cost indollars from the production of X printers is given by C/X=.000xt o005x²+28X+…

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.