Suppose that the marginal propensity to save is ds = 0.95 - dy In(y + 1) (in billions of dollars) y + 1 and that consumption is $6.03 billion when disposable income is $0. Find the national consumption function. C(y) = 6.05

Q: Find the instantaneous rate of change for function at the given value. F(x) = x2 + 2 at x = 0

A: Given a function, F(x) = x2 + 2 at x = 0 To Find the instantaneous rate of change for function at…

Q: Five mice in a stable population of 500 are intentionally infected at r= 0 with a contagious disease…

A:

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: Given An environmentalist find that a certain types of tree grows in such a way that its height h(t)…

Q: Suppose the cost function of a product is given as C=3q -0.0014³. If the cost is increasing at a…

A:

Q: Find the interest earned at 5% compounded continuously for 2 years by a continuous income stream…

A: Given the interest earned r=5%=0.05 , t=2years and PV=1250. We have to find the interest.

Q: Ecologists estimate that, when the population of a certain city is x thousand persons, the average…

A: Given that ,    Ecologist estimate that, when the population of a certain city is x thousand…

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Proceed as shown below...

Q: second. At what rate x changing when x = . O-16 O 16 8 O-8 in such way that the y-value increases at…

A: The given equation is;  y=x3-2x2+x-1.

Q: By choosing small values for h, estimate the instantaneous rate of change of the function f(x) = x³…

A: Use the diffrention formula then simplify

Q: (b) Find the instantaneous rate of change of g with respect to x at x = 3, or state that it does not…

A: 3. given graph of function is                                                       Also,…

Q: A study of a certain Subanen community suggests thatt years from now, the average level of carbon…

A: Given query is to find the rate of change of carbon monoxide after 2 years.

Q: Locate the relative extrema of y = ln(x2 + 2x + 3).

A:

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

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

A:

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: .

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…

A:

Q: s projected that x years from now the population of a certain city will be changing at the rate of…

A:

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: Suppose that h = 2x'y, where both x and y are changing with time. At a certain instant when x = 1…

A:

Q: snip

A: Given: fx=3x-5 To Find: The average rate of change of the given function from x=0 to x=4

Q: Suppose y varies at a constant rate of change of 4 with respect to x (so that Δy=4⋅Δx ), and when…

A: topic - linear equation in two variables

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5/9x² –…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given : A town predicts that its public school population will decrease at the rate of

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

A:

Q: A forester finds that a certain type of forest tree grows in such a way that its height h(t) after t…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given,           Because of job outsourcing, a town predicts that its public school population will…

Q: When air expands adiabatically (without gaining or losingheat), its pressure P and volume V are…

A: Pressure and Volume are related by equation At a instant

Q: Suppose that the revenue (in dollars) from the sale of a product is given by R = 60x + 0.9x? –…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A:

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: projected that, t months from now, the population of a certain town will be growing at the rate of…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x² +…

A: We have to compute backward difference approximations for the first derivative of the function,…

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

A:

Q: The monthly output of a certain product isQ(x) = 2400x5/2where x is the capital investment in…

A: The monthly output of a certain product is Q(x) = 2,400x5/2, where x is the capital investment in…

Q: estimate the instantaneous rate of change at the point indicated.f (x) = ln x; x = 3

A: To find the instantaneous rate of change at x=3 we need f'(3) We find f'(x)

Q: Numerically estimate the instantaneous rate of change of f(x)=e-x^2

A:

Q: A bacterial population B is known to have a rate of growth proportional to B itself. If between noon…

A: Solved below

Q: The rate of increase in the number N of bacteria in a certain culture is given by dN = 0.15N where t…

A:

Q: Assume the rate of investment is given by the function I (t) = ln t. Compute the total capital…

A: We solve this problem by using the capital formation i. e. Total capital accumulation=∫t,t2I(t)dt…

Q: Suppose that the yield (measured in kg/ ha) of an agricultural crop is represented by the function…

A: We need to find rate.

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 that a factory worker starts to make face masks at t = 0 and his rate of change of…

A:

Q: A certain radioactive substance has a half-life of 50 hours. Find how long it will take for 90% of…

A:

Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

A:

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…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: .

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

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.