The number of units Q of a particular commodity that will be produced with K thousand dollars of capital expentiture is modeled by Q(K)= 500K2/3.  Suppose that capital expenditure varies with time in such a way that T months from now there will be K(T) thousand dollars of capital expenditure where K(T)= 2T4+3T+149/T+2.  Also, At what rate will production be changing with respect to time 5 months from now? will the production be increasing or decreasing?

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

A: Given function is as below : C(x)=2x2+6x+12 Marginal cost can be given by Derivative of C(x) .…

Q: 2. A container that has 5 L of water with 1 kg salt dissolved is to be filled by pure water at a…

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Q: Daily crude oil production by one particular oil company for 2008-2013 could be approximated by P (…

A: The given function is Pt=0.009t2-0.7t+3.43. Compute the average rate of change of P ( t ) over the…

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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: A tank contains initially 400 liters of brine holding 100 kg of salt in solution. Water containing…

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Q: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

Q: The volume of fluid in an IV (intravenous) drop decreases according to the mathematical model…

A: The  given model of the volume of fluid in IV drop versus time is:   V=-0.110t+1   Where, V is the…

Q: A tank initially holds 245 liters of brine solution containing 25 Ibm (pound mass) of salt. At t =…

A: Initial amount in tank = 245 liters, in which 25lb Fresh water is poured into @ 7g/m. Well stirred…

Q: f the population of a certain county was 100,000 in 1998 and 110,517 in 2008 and the for- mula y 5…

A: Given, the population of a certain county was 100,000 in 1998 and 110,517 in 2008             and…

Q: ) The population of the world in 2015 was 9.75 billion people and was growing at a rate of 25% per…

A: Given query is to find the expression for the population after t years.

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: Suppose the Marginal product of labor in the economy is given by MPN= .002(16,000-N), while the…

A: a. The market-clearing wage rate equates the demand and supply of labour Solve for w first Therefore…

Q: When a certain product is sold for p dollars per item, consumers will demand D(p)= 12,00p^-1 items…

A: Given, D(p)= 1200p-1 items/week p(t)= 0.5t²+6 dollars/item

Q: Suppose that the demand for a product is given by q2p=6,000, where q represents the number of units…

A:

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A: GIVEN: Height of tall lamppost lights = 20 ft

Q: A study shows that if the government implemented energy conservation measures in 2009, the country's…

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

A: Rate of change is nothing but the change happen in any observations over a period of time. Here…

Q: It is estimated that between the hours of noon and 7:00pm, the speed of highway traffic past a…

A: Check S(t) for all values of t

Q: .

A: We will find the temperature.

Q: A recent report by the U.S. Cen- sus Bureau predicts that the U.S. Hispanic population will increase…

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

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Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 50 + 7x2 + 8y2, where x…

A: Differentiate wrt x and y

Q: The population of a community is growing at 2% per year and its per capita consumption is growing at…

A: Given that: Population growing rate of a community is 2% per year Per capita consumption growth rate…

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

A:

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) her shadow on the…

A: Given query is to y find the rate of change of length of the shadow.

Q: In an extraction unit operating with continuous and counter current, 100 kg of kerosene-nicotine…

A:

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 6x2 + 6y2, where x…

A:

Q: Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt…

A: We need to find amount after one hour.

Q: A point moves along the curve y = x ^ 3−3x + 5 so that x = 1/2√t + 3, where t is time. At what rate…

A: Given- y=x3-3x+5 and x=12t+3 To find- The rate of changing when t=4. Concept Used- dydt=dydx·dxdt

Q: 4. Mauritius island is 2 km due south of its closest point along a straight coastline. Gibril is…

A: Given data:-

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: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Assume that the dynamics of caffeine absorption are given by Ct+1 = 0.87Ct , where t is time in…

A: NOTE: Refresh your page if you can't see any equations. . the given equation is  compare this…

Q: Suppose that the total cost (in dollars) of producing a product is C(x, y) = 15 + 3x2 + 5y2, where…

A: C(x, y) = 15 + 3x2 + 5y2, x is the cost per pound for material and  y is the cost per hour for…

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

A:

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

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Q: Suppose a student is a carrier of the flu virus and returns to his isolated campus of 1000 students.…

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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: One method of slowing the growth of an insect populationwithout using pesticides is to introduce…

A: Given as: Females grows at a rate of  r = 0.10 Number of males S=900 Then:…

Q: 1. There are 64.000 subscribers to an online fashion magazine. Due to competition from a new…

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Q: 9. From 1975 to 2009, the age-adjusted incidence rate of invasive lung and bronchial cancer among…

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Q: 2. A property agent handles an office building with 50 identical offices for rental. Experience…

A: 50 offices occupied corresponding to $800 49 offices corresponding to $820 Plot the two points and…

Q: Suppose that the marginal propensity to consume is dC -0.2y = 0.8 - e dy (in billions of dollars)

A:

Q: (4) Consider the constant rate of decrease of a certain microorganism. At the start, there are…

A: We have to find the number of microorganisms that will be there after 45 seconds.

Q: Suppose a population can be modeled by 50 P(t) = where time is in years since 2005. (1+75e--5t)…

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Q: If f(x) = 5x -3 , compute the instontoneus rate of change of Sx) at x-2. OA -3/49 O8.7/41 oc-7/41…

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Q: Suppose that the fish population P(t) in a lake is attacked by a disease at time t = 0, with the…

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Q: Suppose there is a population of rabbits that (when left alone) experiences population growth at a…

A: Proportionality is between two variables when when they yield fixed ratio, with certain constant…

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.