Suppose that a vending machine service company models its income by assuming that money flows continuously into the machines, with the annual rate of flow given by f(t) = 170e0.03t in thousands of dollars per year. Find the total income from the machines over the first 6 years. (Round your answer to the nearest thousand dollars.)  thousand dollars

Q: A soccer ball manufacturer is planning to expand its workforce. It estimates that the number of…

A:

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: Consider the function that models the number Pt=Aekt=B2tC Here, the objective is to find the…

Q: When the price of a certain commodity isp dollars per unit, customers demand x hundred units of the…

A: Given: x2+3px+p2=79 dpdt=-0.3$/month p=$5

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

A: Proceed as shown below...

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: Put value in function

Q: If the population (in millions) of a country as a function of time (in years) is P(t) = 10 · 2kt,…

A:

Q: Suppose that t years from now, one investment plan will be generating profit at the rate of…

A:

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: Total income over first 8 year is:-

Q: The value of a computer t years after purchase is v(t) = 3000 e -0.35t At what rate is the…

A: Please see the answer in step 2

Q: As an analyst at Decimating Capital, you are asked to estimate the future revenue of the Slate Rock…

A: The revenue function modeled by the equation Rt=0.825t0.04 Here Rt=drtdt Where r(t) is revenue…

Q: The gross domestic product (GDP) of a certain country is projected to  be N(t) = t2 + 2t + 50 ( 0 ≤…

A:

Q: Determine whether the following statements is true or false, and explain why.

A: Given that, ft=1000e0.05t

Q: Suppose that electricity isdraining from a capacitor at a rate that is proportional to the voltageV…

A: Given equation in the question is: Integrating both sides: We have, at t = t0, V  = V0 =>ln(V0)…

Q: A manufacturer of handcrafted wine racks has deter- mined that the cost to produce x units per month…

A: Given: C=0.2x2+10,000

Q: Suppose revenue from the sale of new homes in a certain country decreased dramatically from 2005 to…

A:

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A:

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 770…

A: Given: The cost function is given as, C(x)=770+38x-0.062x2 The objective is to find the rate at…

Q: the number of cell phone subscribers in a certain country in the early 2000s was projected to follow…

A: We use differentiation and integrations to solve this problem.

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 720…

A:

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: Given that, the cost to produce x units per month is given by                C = 0.3x2+8,000  and…

Q: Between 2006 and 2016, the nurmber of applications for patents, N, grew by about 3.6% per year. That…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A:

Q: Find the present value of a continuous income stream F(t) = 20 + 5t, where t is in years and F is in…

A:

Q: Find the present value of a continuous income stream F(t) = 40 + 5t, where t is in years and F is in…

A:

Q: Suppose that the price p (in dollars) and the weekly demand, x (in thousands of units) of a…

A: 6p+x+xp=94,  x=4,  p=9  &  dpdt=2 Differentiating with respect to t (time), we get…

Q: If a baseball is projected upward from ground level with an initial velocity of 160 feet per​…

A:

Q: Suppose revenue from the sale of new homes in a certain country decreased dramatically from 2005 to…

A: Given data: The trend of revenue decrease is, rt=411e-0.321t

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 740…

A: Divide the given function C(x) by the number of units produced ,that is x to obtain the average…

Q: If a baseball is projected upward from ground level with an initial velocity of 32 feet per​…

A: When we throw a ball upwards, that ball goes and goes up, at a certain level of height, the thing is…

Q: Suppose that a business provides a continuous income stream with an annual rate of flow at time t…

A:

Q: Suppose the rate at which consumers purchase peanut butter is increasing at a rate given by  f ′(t)…

A:

Q: The number of traffic accidents per year in a city of population p is predicted to be T 0.002p ³/2.…

A:

Q: For the years from 2002 and projected to 2024, the national health care expenditures H, in billions…

A: H=1,500e^0.053t

Q: When the price of a certain commodity is p dollars per unit, customers demand x hundred units of the…

A:

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: The annual rate of flow given by Total income from the machines over the first 3 years is

Q: A company determines that its total cost, in thousands of 3x rands, for producing x items is C =…

A:

Q: A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of…

A: To determine the counting function P(t) explicitly, under the given conditions

Q: A sample of 300g of lead-210 decays to polonium-210 according to the function given by A(t)=…

A: A sample of 300g of lead-210 decays to polonium-210 according to the function given by A(t)=…

Q: If the total revenue function for a blender is R(x) = 52x − 0.01x2 where x is the number of units…

A: We have the total revenue function R(x) = 52x − 0.01x2.

Q: The total expenditures (in millions) of current dollars for pollution abatement and control during…

A: Here we find the total expenditure.

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: Total money flows in 8 years=…

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: *to find:- total income over the first 3 years. *concept:- integration of e^{ax} = (e^{ax})/a.

Q: A culture contains 1400 bacteria initially and doubles every 50 minutes. Assuming that the rate of…

A: To determine a function P(t) that models the number of bacteria after t minutes.

Q: For the years from 2002 and projected to 2024, the national health care expenditures H, in billions…

A:

Q: Over the next 20 years, a company projects its continuous flow of revenue to be R(x) = 100e01z…

A: Consider the provided question,

Q: A culture contains 2000 bacteria initially and doubles every 40 minutes. Assuming that the rate of…

A:

Q: if the rate of growth of the population of deer in a forest is modeled by R(t)= 2000e^(0.23t) deer…

A: The rate of growth of the population of deer in a forest is modeled by R(t)= 2000e(0.23t) deer per…

Q: Suppose that a vending machine service company models its income by assuming that money flows…

A: The given function is ft=120e0.07t. The total income from machines over first 3 years is obtained by…

Q: Given the function g(x)=x² −2x³ +1, a. Estimate the instantaneous rate of change at x = 1. b. Will…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.