Question 1

If consumption is $4 billion when disposable income is 0, and if the marginal propensity to save is  (in billions of dollars), find the national consumption function. If it's necessary, round your calculations to two decimal places. ​

Accepted Answer

The answer of If consumption is $4 billion when disposable...

Question 2

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is  (in billions of dollars), find the national consumption function. If it's necessary, round your answer to two decimal places. ​

Accepted Answer

The answer of If consumption is $8 billion when disposable...

Question 3

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place. ​

Accepted Answer

The answer of If consumption is $1 billion when disposable...

Question 4

Suppose that the marginal propensity to consume is  (in billions of dollars), and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places. ​

Accepted Answer

The national consumption function is expressed as:
C = a + MPC x Yd
where C is consumption, MPC is the marginal propensity to consume, Yd is disposable income, and a is autonomous consumption (consumption that occurs regardless of income, such as basic needs).
We are given that MPC = 11eb0d3b_9892_c8ea_9790_bf6a481e26d6_TB1243_11 and C = $5.33 billion when Yd = 0.
Substituting these values into the equation, we have:
5.33 = a + 0.11 x 0
a = 5.33
Thus, the national consumption function is:
C = 5.33 + 0.11Yd
Rounding to four decimal places, this can be expressed as:
C = 11eb0d3b_9892_c8ee_9790_8fdc7d64a727_TB1243_11.

Question 5

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars). Round your answer to two decimal places. ​

Accepted Answer

The answer of If consumption C is $1 billion when...

Question 6

Suppose that the marginal cost (in dollars) for a product is  and its fixed cost is $380.00. If the marginal revenue (in dollars) for the product is  , find the profit or loss from production and sale of 35 units. ​

Accepted Answer

The answer of Suppose that the marginal cost (in dollars)...

Question 7

Suppose that the marginal revenue for a certain product is given by  , where x is in thousand of units and revenue is in thousands of dollars. Find  . Round your calculations to two decimal places, if necessary. ​

Accepted Answer

To find marginal revenue, we take the derivative of the revenue function with respect to x. Therefore, we integrate the marginal revenue function with respect to x to find the revenue function. Using the power rule of integration, we get:

Revenue = ∫ 11x dx = 11/2 x^2 + C

where C is the constant of integration. Since the revenue is in thousands of dollars, we need to multiply the expression above by 1000. Also, we know that the revenue is equal to $0 when x = 0, so we can use this information to solve for C. Thus, we have:

0 = 11/2 (0)^2 + C
C = 0

Therefore, the revenue function is:

Revenue = 11/2 x^2

To find the marginal revenue function, we take the derivative of the revenue function with respect to x. Thus:

Marginal revenue = d(11/2 x^2)/dx = 11x

Therefore, the answer is E, 11x.

Question 8

For which of the following differential equations is  a solution? ​

Accepted Answer

The answer of For which of the following differential equations...

Question 9

Use integration to find the general solution to the differential equation  . ​

Accepted Answer

The differential equation 11eb0d3b_9894_019a_9790_59107b082a3f_TB1243_11 can be written as: dy/dx = 2x + 3y We can separate the variables to obtain: dy/ (2x + 3y) = dx Integrating both sides, we get: (1/3) ln|2x + 3y| = x + C where C is the constant of integration. Exponentiating both sides, we obtain: |2x + 3y| = e^(3x+3C) Since the absolute value of 2x + 3y can take two values depending on the sign of 2x + 3y, we consider two cases: Case 1: 2x + 3y > 0 In this case, we have: 2x + 3y = e^(3x+3C) Solving for y, we get: y = (1/3) (e^(3x+3C) - 2x) Case 2: 2x + 3y < 0 In this case, we have: -2x - 3y = e^(3x+3C) Solving for y, we get: y = (1/3) (-e^(3x+3C) - 2x) Therefore, the general solution is: y = (1/3) (e^(3x+3C) - 2x) if 2x + 3y > 0 y = (1/3) (-e^(3x+3C) - 2x) if 2x + 3y < 0

Question 10

The average cost of a product, in dollars, changes at the rate  and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent. ​

Accepted Answer

The answer of The average cost of a product, in...

Question 11

Use integration to find the general solution to the differential equation  . ​

Accepted Answer

Taking the antiderivative of both sides gives:
$$\int \frac{\mathrm{d}y}{\sqrt{1-y^2}} = \int \frac{x^2}{\sqrt{1-x^6}}\,\mathrm{d}x$$
The left-hand side can be evaluated by the substitution $y=\sin u$, $\mathrm{d}y = \cos u\,\mathrm{d}u$:
$$\int \frac{\mathrm{d}y}{\sqrt{1-y^2}} = \int \frac{\cos u}{\sqrt{1-\sin^2 u}}\,\mathrm{d}u = \int \mathrm{d}u = u + C_1$$
where $C_1$ is the constant of integration. The right-hand side can be evaluated by the substitution $x^6 = \frac{1}{t^2}$, $6x^5\,\mathrm{d}x = -\frac{2}{t^3}\,\mathrm{d}t$:
\begin{align*}
\int \frac{x^2}{\sqrt{1-x^6}}\,\mathrm{d}x &= -\frac{1}{3}\int \frac{\mathrm{d}t}{t\sqrt{t^4-1}} \
&= -\frac{\mathrm{arsinh}\left(t^2ight)}{3} + C_2 \
&= -\frac{\mathrm{arsinh}\left(\frac{1}{x^3}ight)}{3} + C_2
\end{align*}
where $\mathrm{arsinh}$ denotes the inverse hyperbolic sine function, and $C_2$ is another constant of integration. Therefore, the general solution is given by:
$$\mathrm{arsinh}\left(\frac{1}{x^3}ight) = -3u + C$$
where $C=C_1+C_2$ is the combined constant of integration.

Question 12

If consumption is $6.3 billion when disposable income is 0, and if the marginal propensity to consume is  (in billions of dollars), find the national consumption function. If it's necessary, round your calculations to three decimal places. ​

Accepted Answer

The answer of If consumption is $6.3 billion when disposable...

Question 13

Suppose that the marginal propensity to consume is  (in billions of dollars) and that consumption is $5.35 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Accepted Answer

We know that the consumption function is given by: 
C = a + b(Yd)
where, 
C = consumption
a = autonomous consumption
b = marginal propensity to consume (MPC)
Yd = disposable income

We are given that when disposable income is 0, consumption is $5.35 billion. This implies that autonomous consumption is $5.35 billion (because there is no disposable income to consume). Hence, we have:
a = 5.35

We are also given that MPC = 0.11. Hence, we have:
b = 0.11

Therefore, the consumption function is:
C = 5.35 + 0.11Yd

Hence, the answer is B.

Question 14

Find the particular solution. ​  ​

Accepted Answer

The answer of Find the particular solution. ​  ​
...

Question 15

The average cost of a product changes at the rate  and the average cost of 12 units is $18.00. Find the average cost function  . ​

Accepted Answer

The answer of The average cost of a product changes...

Question 16

Suppose that the marginal cost for a certain product is given by  , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $210,000. Find  . Round your answer to three decimal places, if necessary. ​

Accepted Answer

The answer of Suppose that the marginal cost for a...

Question 17

Suppose that the marginal propensity to save is  (in billions of dollars) and that consumption is $9 billion when disposable income is 0. Find the national consumption function C. Round numbers in our answer to two decimal places when appropriate. If it's necessary, round your calculations to two decimal places. ​

Accepted Answer

The answer of Suppose that the marginal propensity to save...

Question 18

Suppose that the marginal propensity to save is  (in billions of dollars), and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places. ​

Accepted Answer

The answer of Suppose that the marginal propensity to save...

Question 19

Consider the following function:  . Of which of the following differential equations is this a solution? ​

Accepted Answer

The answer of Consider the following function:  . Of...

Question 20

Use integration to find the general solution to the differential equation  . ​

Accepted Answer

The answer of Use integration to find the general solution...

Quiz 13: Indefinite Integrals

If consumption is $4 billion when disposable income is 0, and if the marginal propensity to save is (in billions of dollars) , find the national consumption function. If it's necessary, round your calculations to two decimal places.

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars) , find the national consumption function. If it's necessary, round your answer to two decimal places.

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place.

Suppose that the marginal propensity to consume is (in billions of dollars) , and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places.

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars) . Round your answer to two decimal places.

Suppose that the marginal cost (in dollars) for a product is and its fixed cost is $380.00. If the marginal revenue (in dollars) for the product is , find the profit or loss from production and sale of 35 units.

Suppose that the marginal revenue for a certain product is given by , where x is in thousand of units and revenue is in thousands of dollars. Find . Round your calculations to two decimal places, if necessary.

For which of the following differential equations is a solution?

Use integration to find the general solution to the differential equation .

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent.

Use integration to find the general solution to the differential equation .

If consumption is $6.3 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars) , find the national consumption function. If it's necessary, round your calculations to three decimal places.

Suppose that the marginal propensity to consume is (in billions of dollars) and that consumption is $5.35 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Find the particular solution.

The average cost of a product changes at the rate and the average cost of 12 units is $18.00. Find the average cost function .

Suppose that the marginal cost for a certain product is given by , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $210,000. Find . Round your answer to three decimal places, if necessary.

Suppose that the marginal propensity to save is (in billions of dollars) , and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places.

Consider the following function: . Of which of the following differential equations is this a solution?

Use integration to find the general solution to the differential equation .

Quiz 13: Indefinite Integrals

If consumption is $4 billion when disposable income is 0, and if the marginal propensity to save is (in billions of dollars) , find the national consumption function. If it's necessary, round your calculations to two decimal places. ​

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars) , find the national consumption function. If it's necessary, round your answer to two decimal places. ​

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place. ​

Suppose that the marginal propensity to consume is (in billions of dollars) , and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places. ​

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars) . Round your answer to two decimal places. ​

Suppose that the marginal cost (in dollars) for a product is and its fixed cost is $380.00. If the marginal revenue (in dollars) for the product is , find the profit or loss from production and sale of 35 units. ​

Suppose that the marginal revenue for a certain product is given by , where x is in thousand of units and revenue is in thousands of dollars. Find . Round your calculations to two decimal places, if necessary. ​

For which of the following differential equations is a solution? ​

Use integration to find the general solution to the differential equation . ​

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent. ​

Use integration to find the general solution to the differential equation . ​

If consumption is $6.3 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars) , find the national consumption function. If it's necessary, round your calculations to three decimal places. ​

Suppose that the marginal propensity to consume is (in billions of dollars) and that consumption is $5.35 billion when disposable income is 0. Find the national consumption function C. If it's necessary, round your calculations to two decimal places.

Find the particular solution. ​ ​

The average cost of a product changes at the rate and the average cost of 12 units is $18.00. Find the average cost function . ​

Suppose that the marginal cost for a certain product is given by , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $210,000. Find . Round your answer to three decimal places, if necessary. ​

Suppose that the marginal propensity to save is (in billions of dollars) , and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places. ​

Consider the following function: . Of which of the following differential equations is this a solution? ​

Use integration to find the general solution to the differential equation . ​

If consumption is $4 billion when disposable income is 0, and if the marginal propensity to save is (in billions of dollars) , find the national consumption function. If it's necessary, round your calculations to two decimal places.

If consumption is $8 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars) , find the national consumption function. If it's necessary, round your answer to two decimal places.

If consumption is $1 billion when disposable income is 0, and if the marginal propensity to consume is 0.50, what is consumption when disposable income is 50 billion? If it's necessary, round your answer to one decimal place.

Suppose that the marginal propensity to consume is (in billions of dollars) , and that consumption is $5.33 billion when disposable income is 0. Find the national consumption function. If it's necessary, round your calculations to four decimal places.

If consumption C is $1 billion when disposable income y is 0, and if the marginal propensity to consume is 0.60, find the national consumption function C as a function of y (in billions of dollars) . Round your answer to two decimal places.

Suppose that the marginal cost (in dollars) for a product is and its fixed cost is $380.00. If the marginal revenue (in dollars) for the product is , find the profit or loss from production and sale of 35 units.

Suppose that the marginal revenue for a certain product is given by , where x is in thousand of units and revenue is in thousands of dollars. Find . Round your calculations to two decimal places, if necessary.

For which of the following differential equations is a solution?

Use integration to find the general solution to the differential equation .

The average cost of a product, in dollars, changes at the rate and the average cost of 12 units is $25.00. Find the average cost of 24 units. Round your answer to the nearest cent.

Use integration to find the general solution to the differential equation .

If consumption is $6.3 billion when disposable income is 0, and if the marginal propensity to consume is (in billions of dollars) , find the national consumption function. If it's necessary, round your calculations to three decimal places.

Find the particular solution.

The average cost of a product changes at the rate and the average cost of 12 units is $18.00. Find the average cost function .

Suppose that the marginal cost for a certain product is given by , where x is in thousand of units and cost is in thousands of dollars. Suppose further that fixed costs are $210,000. Find . Round your answer to three decimal places, if necessary.

Suppose that the marginal propensity to save is (in billions of dollars) , and that consumption is $8.30 billion when disposable income is 0. Find the national consumption function. Round your answer to two decimal places.

Consider the following function: . Of which of the following differential equations is this a solution?

Use integration to find the general solution to the differential equation .