Question 1

Determine whether the equation defines y as a linear function of x.

Accepted Answer

The answer of Determine whether the equation defines y as...

Question 2

Entomologists have discovered that a linear relationship exists between the number of chirps of crickets of a certain species and the air temperature. When the temperature is  the crickets chirp at the rate of 80 times/minute, and when the temperature is  they chirp at the rate of 160 times/minute. Find an equation giving the relationship between the air temperature T and the number of chirps/minute N of the crickets.

Accepted Answer

The answer of Entomologists have discovered that a linear relationship...

Question 3

The number of homes with digital TVs is expected to grow according to the function  where t is measured in years, with t = 0 corresponding to the beginning of 2000, and f(t) is measured in millions of homes. How many homes had digital TVs at the beginning of 2000?

Accepted Answer

The answer of The number of homes with digital TVs...

Question 4

Suppliers of transistor radios will market 10,000 units when the unit price is $55 and 62,500 units when the unit price is $100. Determine the supply function if it is known to have the form  where x is the quantity supplied and p is the unit price in dollars.

Accepted Answer

The answer of Suppliers of transistor radios will market 10,000...

Question 5

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by  where x denotes the number of units manufactured each month. What is Apollo's revenue when 1,500 units are produced?

Accepted Answer

The answer of The revenue (in dollars) realized by Apollo...

Question 6

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function.

Accepted Answer

We cannot determine whether the function is a polynomial or rational function since there is no given function. The given code (11eaa8b1_dc8c_bc85_b1b6_b915a48728db_TB6026_11) appears to be some sort of identifier or placeholder, but it is not a mathematical function. Therefore, option A is the correct answer.

Question 7

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

Accepted Answer

To find m and b, use the given points: f(0) = 8 gives b = 8. For f(1) = 4, substitute into f(x) = mx + b: 4 = m(1) + 8, solving gives m = -4.

Question 8

Economists define the disposable annual income for an individual by the equation D = (1 - r)T, where T is the individual's total income and r is the net rate at which he or she is taxed. What is the disposable income for an individual whose income is $90,000 and whose net tax rate is 35%?

Accepted Answer

Given, 
T (total income) = $90,000 
r (net tax rate) = 35%

Using the formula, 
D (disposable income) = (1 - r)T
D = (1 - 0.35) x $90,000
D = 0.65 x $90,000
D = $58,500

Therefore, the disposable income for the individual is $58,500. Option B is correct.

Question 9

For the supply equation  where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 3 units of the commodity available in the market.

Accepted Answer

The answer of For the supply equation  where x...

Question 10

The owner of a luxury motor yacht that sails among the 4,000 Greek islands charges $800/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then each fare is reduced by $4 for each additional passenger. Assume at least 20 people sign up for the cruise and let x denote the number of passengers above 20. Find a function R giving the revenue/day realized from the charter.

Accepted Answer

The answer of The owner of a luxury motor yacht...

Question 11

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.
X = 5y - 25

Accepted Answer

The answer of Determine whether the equation defines y as...

Question 12

For the demand equation  where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, determine the quantity demanded when the unit price is set at $6.

Accepted Answer

Substitute p=6 in the demand equation: 
x = (11/6)e^(0.8(6)) = 3000 units. 
Therefore, the quantity demanded when the unit price is $6 is 3000 units.

Question 13

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function.

Accepted Answer

The answer of Determine whether the given function is a...

Question 14

For the supply equation  where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 4 units of the commodity available in the market.

Accepted Answer

The answer of For the supply equation  where x...

Question 15

For the demand equation  where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, select the demand curve.

Accepted Answer

The answer of For the demand equation  where x...

Question 16

The ratio of working-age population to the elderly in the United States (including projections after 2000) is given by  with t = 0 corresponding to the beginning of 1995. What will be the ratio at the beginning of 2005?

Accepted Answer

We need to evaluate the function for t=10, which corresponds to the beginning of 2005:

f(10) = 11e^(0.035x10) = 11e^0.35

Using a calculator, we find that:

f(10) ≈ 3.9

Therefore, the ratio of working-age population to the elderly at the beginning of 2005 was approximately 3.9. The correct answer is (E).

Question 17

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function.

Accepted Answer

Without any additional information about the function, we cannot determine its degree or whether it is a polynomial or rational function. However, we can rule out choices A, B, and C because they all assume that the function is a polynomial function. The correct answer is D, as it is the only option that allows for the function to be either a polynomial or a rational function.

Question 18

Accepted Answer

The answer of 
...

Question 19

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $40/unit. What is the cost function? What is the revenue function? What is the profit function?

Accepted Answer

- The cost function is given by: C(x) = fixed cost + variable cost per unit * number of units produced = 45,000 + 9x, where x is the number of units produced.
- The revenue function is given by: R(x) = price per unit * number of units sold = 40x, where x is the number of units sold.
- The profit function is given by: P(x) = revenue - cost = R(x) - C(x) = 40x - (45,000 + 9x) = 31x - 45,000.
Therefore, the correct choice is A.

Question 20

For the supply equations, where x is the quantity supplied in units of a thousand and p is the unit price in dollars, sketch the supply curve.

Accepted Answer

The supply curve has a positive slope meaning as the price increases, the quantity supplied also increases. Based on the equation given, the coefficient of x should be positive while the constant term should be zero or negative. Among the choices, only C satisfies these conditions.

Quiz 2: Functions, Limits and the Derivative

Determine whether the equation defines y as a linear function of x.

The number of homes with digital TVs is expected to grow according to the function where t is measured in years, with t = 0 corresponding to the beginning of 2000, and f(t) is measured in millions of homes. How many homes had digital TVs at the beginning of 2000?

Suppliers of transistor radios will market 10,000 units when the unit price is $55 and 62,500 units when the unit price is $100. Determine the supply function if it is known to have the form where x is the quantity supplied and p is the unit price in dollars.

The revenue (in dollars) realized by Apollo from the sale of its inkjet printers is given by where x denotes the number of units manufactured each month. What is Apollo's revenue when 1,500 units are produced?

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function.

Find the constants m and b in the linear function f (x) = mx + b, so that f (0) = 8 and f (1) = 4.

Economists define the disposable annual income for an individual by the equation D = (1 - r) T, where T is the individual's total income and r is the net rate at which he or she is taxed. What is the disposable income for an individual whose income is $90,000 and whose net tax rate is 35%?

For the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 3 units of the commodity available in the market.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. X = 5y - 25

For the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, determine the quantity demanded when the unit price is set at $6.

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function.

For the supply equation where x is the quantity supplied in units of a thousand and p is the unit price in dollars, determine the price at which the supplier will make 4 units of the commodity available in the market.

For the demand equation where x represents the quantity demanded in units of a thousand and p is the unit price in dollars, select the demand curve.

The ratio of working-age population to the elderly in the United States (including projections after 2000) is given by with t = 0 corresponding to the beginning of 1995. What will be the ratio at the beginning of 2005?

Determine whether the given function is a polynomial function or rational function. State the degree, if it is a polynomial function.

A manufacturer has a monthly fixed cost of $45,000 and a production cost of $9 for each unit produced. The product sells for $40/unit. What is the cost function? What is the revenue function? What is the profit function?

For the supply equations, where x is the quantity supplied in units of a thousand and p is the unit price in dollars, sketch the supply curve.