Suppose the marginal propensity to consume is given by: DC/DY=.03- .2/Square root of (y), (in billions of dollars)  and national consumption is $8 billion when disposable income is $0. Find the national consumption function.

Q: At which points on the curve y = 1+40x3 – 3x does the tangent line have a locally maximum slope? A…

A: Solve the following

Q: If the instantaneous rate of change of f(x) at (8, −7) is 9, write the equation of the line tangent…

A: It's given that the instantaneous rate of change  of  f(x) at  (8,-7) is 9 . We have to find the…

Q: If the instantaneous rate of change of f(x) at (5,-9) is 3, write the equation of the line tangent…

A: For equation of tangent, one have to use y-b=m(x-a)Where (a,b) is the point, m is the slope.

Q: If the revenue function for a certain commodity is R(x) = 45x/lnx compute the marginal revenue when…

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Q: find the slope of the tangent to the curve of f(x)= 1/square root of x at the point where x=1/4

A: Topic:- application of derivatives

Q: Suppose that the total cost in dollars of producing x units of a product is given by C(x) = 10,000 +…

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

A:

Q: Suppose the total cost (in dollars) for a product is given by `C(x)=200x+20\ln(x)` where `x` is the…

A:

Q: If a manufacturer's average cost equation is 200 + 48q° What is the marginal cost when 17 units are…

A: Solution is given below:

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: Find the slope of the tangent line to the graph of the functiony=f(x)=−6.5x^2 at point x=7

A:

Q: 2. Suppose that the marginal revenue for a company manufacturing coffee machines is given by…

A: Given expression for marginal revenue of the company is: Q=100-0.5x where, Q is the marginal revenue…

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: Suppose that the cost of producing x items is C(x) = .005x3 - .5x2 + 28x + 300 dollars, and daily…

A: Cx=0.005x3-0.5x2+28x+300 a). The extra cost of increasing daily production from 50 to 51 items is,…

Q: what is the marginal revenue function at x=1?

A:

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: If the marginal revenue (in dollars per unit) for a month for a commodity is MR = -0.6x + 23, find…

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Q: Suppose that the marginal propensity to save is SP = 0.1 - dy (in billions of dollars) 7y + 2 and…

A: Given: The marginal propensity is The consumption is $ 7 billion and the disposable income is $ 0

Q: the correct formula for marginal profit is

A: Given  the correct formula for marginal profit is

Q: What is the concentration of glucose in the bloodstream after 10 min if r =5 g per min, k = 5, and…

A:

Q: 4. Suppose that the marginal propensity to consume is dc 0.7-ey (in billions of dollars) dy and that…

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Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

Q: Suppose that the total cost in dollars of producing x units of a product is given by C(x) = 5,000 +…

A:

Q: Find the equation of the line tangent to the graph of f(x)=(lnx)^2 at x=3.

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Q: A company estimates that the marginal cost (in dollars per item) of producing a items is 1.92…

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

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Q: If the marginal revenue (in dollars per unit) for a month for a commodity is  MR = −0.6x + 41,…

A: Revenue fuction=∫MRdx +c

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

A:

Q: If total revenue is R=50Q-2Q^2. At what value of Q will marginal revenue by -10?

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Q: If the marginal revenue (in dollars per unit) for a month for a commodity is MR = −0.6x + 35, find…

A:

Q: find the marginal revenue at a production level of 1,600 pairs  x= 4,000- 40p

A: To find marginal revenue , first find out the revenue function using the given equation. Solve the…

Q: A liquid form of antibiotic manufactured by a pharmaceutical firm is sold in bulk with a total…

A: Total production cost : C(x)=500,000+80x+0.003x2

Q: Find the marginal revenue function.

A:

Q: Suppose that Omar's marginal utility for cups of coffee is constant at 1.5 utils per cup no matter…

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Q: Suppose that the monthly cost, in dollars, of producing x chairs is C(x) = 0.001x° +0.07x + 14x +…

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Q: Find the equation of the line tangent to the graph f(x)= (lnx)5 at x=5

A: First find slope then use equation of tangent tangent line

Q: At a certain factory, the marginal cost is 3(q - 4)2 dollars per unit when the level of production…

A: Consider the given marginal cost function as M(q) = 3(q-4)2 Let C(q) denote the total cost of…

Q: Suppose that value of wine respect to time is given following function V = 100e ve. How long will it…

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 daily profit (in dollars) from the production and sale of x units of a product is…

A:

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

A:

Q: Let’s assume that in Kansas, a family farmer sells wheat in a perfectly competitive market. After…

A: Given After increasing the production of wheat from 220 bushels to 240 bushels, the total revenue of…

Q: A company estimates that the marginal cost (in dollars per item) of producing x items is 0.006x. If…

A:

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

A:

Q: Suppose that the marginal propensity to save is ds = 0.95 - dy In(y + 1) (in billions of dollars) y…

A: According to question given :dSdy=0.95-lny+1y+1Consumption is $6.03 when disposable income is $0

Q: If the instantaneous rate of change of f(x) at (6, −8) is 4, write the equation of the line tangent…

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.