Question 1

The number of persons aged 18-64 receiving disability benefits through Social Security, the Supplemental Security income, or both, from 1990 through 2000 is approximated by the function  where  is measured in units of a million and t is measured in years, with t = 0 corresponding to the beginning of 1990.
Compute  .Round the answers to the nearest thousandth.  __________ million  __________ million per year  __________ million per year in the second power

Accepted Answer

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Question 2

The consumption function of the U.S.economy from 1929 to 1941 is  , where  is the personal consumption expenditure and  is the personal income, both measured in billions of dollars.Find the rate of change of consumption with respect to income,  .This quantity is called the marginal propensity to consume.

Accepted Answer

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Question 3

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system.The marketing department has determined that the demand for these speakers is  , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the marginal revenue function  .

Accepted Answer

The marginal revenue function is given by the derivative of the demand function with respect to quantity, multiplied by the unit price plus the demand function. Mathematically,
MR(x) = (dp/dx) * p + D(x)
Where D(x) = 11eb12b0_aa1d_1a79_b394_9dcb386a2a5d_TB7866_11 is the demand function and p is the unit price.

Taking the derivative of the demand function, we get
dp/dx = -2x/1000

Plugging this back into the marginal revenue function, we get
MR(x) = (-2xp/1000) + 11eb12b0_aa1d_1a79_b394_9dcb386a2a5d_TB7866_11

Simplifying, we get
MR(x) = 11eb12b0_aa1d_1a7c_b394_33437eafacc7_TB7866_11

Therefore, the correct choice is B.

Question 4

The demand equation for the Roland portable hair dryer is given by  , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars.When is the demand unitary? (Hint: Solve  for p).

Accepted Answer

To find the unitary demand, we need to solve the equation for p such that the price elasticity of demand equals -1. So, we start by taking the derivative of the demand equation with respect to p and multiplying by p/x:
p/x * dQ/dp = -11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11

Simplifying, we get:
p/x = -11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11 * Q/p

Multiplying both sides by p^2/Q, we get:
p = (-11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11)^(1/2) * (Q^(1/2))

Substituting Q = x * 100 and simplifying, we get:
p = (-11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11)^(1/2) * (100x)^(1/2)

To find the unitary demand, we need the price that corresponds to a price elasticity of -1. This occurs when the absolute value of the elasticity is equal to 1, so:
|dQ/dp * p/Q| = 1
|(-11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11)^(1/2) * (100x)^(-1/2) * p/Q| = 1
(-11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11)^(1/2) * (100x)^(-1/2) * p/Q = 1 or -1

Solving for p, we get:
p = (-11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11)^(1/2) * (100x)

Since p is measured in dollars, we can write the price as:
p = kx, where k = (-11eb12b0_aa16_b197_b394_ff71a1cb24c9_TB7866_11)^(1/2) * 100

This means that the demand is unitary when the price is equal to kx. So, the correct answer is choice B.

Question 5

Find the third derivative of the function.

Accepted Answer

The answer of Find the third derivative of the function....

Question 6

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be  .The demand equation is  .Select the graph of the profit function.

Accepted Answer

The answer of Acrosonic's production department estimates that the total...

Question 7

The proprietor of the Showplace, a video store, has estimated that the rental price p (in dollars) of prerecorded video discs is related to the quantity x rented/day by the demand equation  Currently, the rental price is $2/disc.Is the demand elastic or inelastic at this rental price? If the rental price is increased, will the revenue increase or decrease?

Accepted Answer

The answer of The proprietor of the Showplace, a video...

Question 8

Custom Office makes a line of executive desks.It is estimated that the total cost for making x units of their Senior Executive model is  dollars/year. Find the average cost function C.

Find the marginal average cost function

Accepted Answer

The answer of Custom Office makes a line of executive...

Question 9

Find the third derivative of the function.

Accepted Answer

The answer of Find the third derivative of the function....

Question 10

Williams Commuter Air Service realizes a monthly revenue of  dollars when the price charged per passenger is x dollars. Find the marginal revenue  .

Accepted Answer

The answer of Williams Commuter Air Service realizes a monthly...

Question 11

The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is  dollars/year. Find the average cost function C.

Accepted Answer

The answer of The management of ThermoMaster Company, whose Mexican...

Question 12

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by  . What is the marginal average cost function  ?

Accepted Answer

The marginal average cost function can be found by taking the derivative of the total cost function with respect to the quantity (number of units produced), and then dividing that by the quantity.

Taking the derivative of the total cost function, we get:
MC(q) = 2q + 25

Dividing that by the quantity, we get:
MAC(q) = (2q + 25)/q

Simplifying this expression, we get:
MAC(q) = 2 + (25/q)

Therefore, the correct answer is B.

Question 13

Find the third derivative of the function.

Accepted Answer

The answer of Find the third derivative of the function....

Question 14

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was  percent of the original amount.Compute  .Round the answers to the nearest thousandth.  __________% per minute  __________% per minute in the second power

Accepted Answer

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Question 15

During the construction of an office building, a hammer is accidentally dropped from a height of 16 ft.The distance the hammer falls in t sec is  .What is the hammer's velocity when it strikes the ground? What is its acceleration?
The velocity is __________ ft per second.
The acceleration is __________ ft per second in the second power.

Accepted Answer

The answer of During the construction of an office building,...

Question 16

Pulsar manufactures a series of 19-in.color television sets.The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation  .The weekly total cost incurred by Pulsar for producing x sets is  dollars.Compute  ,  ,  .

Accepted Answer

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Question 17

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is  . What is the marginal cost when  and  ?

Accepted Answer

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Question 18

Custom Office makes a line of executive desks.It is estimated that the total cost for making x units of their Senior Executive model is  dollars/year. Find the marginal average cost function  .

Accepted Answer

The answer of Custom Office makes a line of executive...

Question 19

A division of Ditton Industries manufactures the Futura model microwave oven.The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced.What is the actual cost incurred in manufacturing the 301^st oven and the marginal cost when ?

Accepted Answer

The answer of A division of Ditton Industries manufactures the...

Question 20

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system.The marketing department has determined that the demand for these speakers is  , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be  .
Find the profit function P and select the graph of the profit function.

Accepted Answer

The answer of The management of Acrosonic plans to market...

Quiz 3: Differentiation

The management of Acrosonic plans to market the ElectroStat, an electrostatic speaker system.The marketing department has determined that the demand for these speakers is , where p denotes the speaker's unit price (in dollars) and x denotes the quantity demanded. Find the marginal revenue function .

The demand equation for the Roland portable hair dryer is given by , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars.When is the demand unitary? (Hint: Solve for p) .

Find the third derivative of the function.

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be .The demand equation is .Select the graph of the profit function.

Custom Office makes a line of executive desks.It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the average cost function C. Find the marginal average cost function

Find the third derivative of the function.

Williams Commuter Air Service realizes a monthly revenue of dollars when the price charged per passenger is x dollars. Find the marginal revenue .

The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is dollars/year. Find the average cost function C.

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by . What is the marginal average cost function ?

Find the third derivative of the function.

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was percent of the original amount.Compute .Round the answers to the nearest thousandth. % per minute % per minute in the second power

Pulsar manufactures a series of 19-in.color television sets.The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation .The weekly total cost incurred by Pulsar for producing x sets is dollars.Compute , , .

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is . What is the marginal cost when and ?

Custom Office makes a line of executive desks.It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the marginal average cost function .

A division of Ditton Industries manufactures the Futura model microwave oven.The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced.What is the actual cost incurred in manufacturing the 301^st oven and the marginal cost when ?

Quiz 3: Differentiation

The demand equation for the Roland portable hair dryer is given by , where x (measured in units of a hundred) is the quantity demanded per week and p is the unit price in dollars.When is the demand unitary? (Hint: Solve for p) .

Find the third derivative of the function.

Acrosonic's production department estimates that the total cost (in dollars) incurred in manufacturing x ElectroStat speaker systems in the first year of production will be .The demand equation is .Select the graph of the profit function.

Custom Office makes a line of executive desks.It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the average cost function C. Find the marginal average cost function

Find the third derivative of the function.

Williams Commuter Air Service realizes a monthly revenue of dollars when the price charged per passenger is x dollars. Find the marginal revenue .

The management of ThermoMaster Company, whose Mexican subsidiary manufactures an indoor-outdoor thermometer, has estimated that the total weekly cost (in dollars) for producing x thermometers is dollars/year. Find the average cost function C.

The weekly total cost function associated with manufacturing the Pulsar 25 color console television is given by . What is the marginal average cost function ?

Find the third derivative of the function.

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was percent of the original amount.Compute .Round the answers to the nearest thousandth. __________% per minute __________% per minute in the second power

Pulsar manufactures a series of 19-in.color television sets.The quantity x of these sets demanded each week is related to the wholesale unit price p by the equation .The weekly total cost incurred by Pulsar for producing x sets is dollars.Compute , , .

The total weekly cost (in dollars) incurred by a company in pressing x compact discs is . What is the marginal cost when and ?

Custom Office makes a line of executive desks.It is estimated that the total cost for making x units of their Senior Executive model is dollars/year. Find the marginal average cost function .

A division of Ditton Industries manufactures the Futura model microwave oven.The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced.What is the actual cost incurred in manufacturing the 301st oven and the marginal cost when ?

During testing of a certain brand of air purifier, the amount of smoke remaining t min after the start of the test was percent of the original amount.Compute .Round the answers to the nearest thousandth. % per minute % per minute in the second power

A division of Ditton Industries manufactures the Futura model microwave oven.The daily cost (in dollars) of producing these microwave ovens is where x stands for the number of units produced.What is the actual cost incurred in manufacturing the 301^st oven and the marginal cost when ?