A 57-year-old couple is considering opening a business of their own. They will either purchase an established Gift and Card Shoppe or open a new Wine Boutique. The Gift Shoppe has a continuous income stream with an annual rate of flow at time t given by G(t) = 35,500    (dollars per year). The Wine Boutique has a continuous income stream with a projected annual rate of flow at time t given by W(t) = 20,200e0.08t    (dollars per year). The initial investment is the same for both businesses, and money is worth 10% compounded continuously. Find the present value of each business over the next 8 years (until the couple reaches age 65) to see which is the better buy. (Round your answers to the nearest dollar.)   Gift Shoppe $   Wine Boutique      $

Q: If a town has a population of 850 people at year t=0, what is the formula for if it grows at a…

A:

Q: 20. In "x" years from now, one investment plan will be generating profit at the rate of R₁ (x) = 50+…

A: Given: R1x=50+x2R2x=200+5x

Q: Find the consumers surplus if the demand function for a particular beverage is given by…

A: The consumer surplus is given by C.S.=∫q=0q=eDq dq -e·De, where e is equilibrium value of q. Here,…

Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

A:

Q: in the early 1970s there were approximately 40,000 trees lining the streets of Newton. Today, that…

A:

Q: A tank initially holds 245 liters of brine solution containing 25 Ibm (pound mass) of salt. At t =…

A: Initial amount in tank = 245 liters, in which 25lb Fresh water is poured into @ 7g/m. Well stirred…

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

A: Given the income function as, ft=24,000e0.05t.

Q: Find the linearization of y = at x = 16.

A:

Q: Find the present value of a continuous stream of income over 3 years if the rate of income is…

A: Given the rate of income , ft=80e-0.08t Number of yearsT=3 Interest rater=11% The present value can…

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

A:

Q: 5. 2 x' = 3 х, 1 x(0) = 1

A: In this question, we have to find the general solution of the differential equation and draw the…

Q: Find the present value P of a continuous income flow of c(t) dollars per year using c(t)e-rt dt, J-…

A:

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

A: Monthly rate flow is , f(t)=36,000e0.03t. "t" denotes number of months. We have to find for 12…

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

A: Given ft=36,000e0.06t The given function gives the income at t months. The function that gives the…

Q: Find the demand function x = f(p) that satisfies the initial conditions. dx 800 x = 20,000 when p =…

A:

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

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

Q: Suppose that we were to model a continuous income stream using the function f(t)=t2 / (t-1)(t+1) for…

A: The function that models a continuous income stream is

Q: Suppose that a steel company views the production of its continuous caster as a continuous income…

A:

Q: Suppose that a population has a rate of growth of 0.1 and a carrying ranacity of 2 million, Şet up…

A: The population dynamics can be modeled through a first-order differential equation. It contains the…

Q: (For Bacteriologists). In one of your Basic Calculus sessions, a top of the class Grade- 12 student…

A: Hair we have to find out the value of Y for the different values of T

Q: 4. Find the general form of the function that satisfies dP/dt = -3P(t).

A: A separable differential equation can be solved by separating the terms in each variable and…

Q: find the absolute maximum and minimumvalues of each function on the given interval. y = x ln 2x - x,…

A: We have to find absolute maximum and minimum values of the given function y=xln2x-x, on the interval…

Q: Suppose that I years from now, one investment plan will be generating profit at the rate of P1'(t)=…

A: Given. P1'(t) = 90e0.1t (1000$) P2'(t) = 140e0.07t (1000$)

Q: If population y grows at a rate proportional to the current population, then y could be

A: This make separable differential equation

Q: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

A: Given problem:- The population of the world in 2015 was 9.75 billion people and was growing at a…

Q: the demand function for a particular beverage is given by D(q)=(3000)/((3q+2)^(2)) and if the supply…

A:

Q: Find the​ consumers' surplus if the demand function for a particular beverage is given by…

A: We are given the demand function for a particular beverage as: D(q) = p=30003q+72 The equilibrium…

Q: Find the present value P of a continuous income flow of c(t) dollars per year using where t1 is the…

A: Given, c(t)=100,000+4000, r=5%, t1=10 p=∫0t1c(t)e-rtdt Now plug the values of t1  and r…

Q: A continuous stream of income is being produced at the constant rate of $8,000 per year. Find the…

A: Given, A continuous stream of income is being produced at the constant rate of $8,000 per year.We…

Q: The city of Anville is currently home to 30000 people, and the population has been growing at a…

A:

Q: Find the maximum rate of change of the function f(x,y) =4x^2-2y^3 at the point (1,1)

A: Given data: The given function is f(x,y)=4x2-2y3. The given point is (a, b)=(1, 1). The expression…

Q: Consider three connected lakes, A, B, and C, where lake B has a volume of 2650 km3, and water flows…

A: Here we have consider 3 lakes. i.e A,B and C.                               Volume of lake B=2650…

Q: A small brewery considers the output of its bottling machine as a continuous income stream with an…

A: According to the total income of Continuous Income Stream: If the rate of receipt of revenue is ft…

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: In an extraction unit operating with continuous and counter current, 100 kg of kerosene-nicotine…

A:

Q: Find the demand function x = f(p) that satisfies the initial conditions. dx 600 x = 15,000 when p =…

A:

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

A:

Q: The city of Anville is currently home to 23000 people, and the population has been growing at a…

A:

Q: A certain population of bacteria is known to grow at a rate proportional to the amount present in a…

A:

Q: suppose that a five year rate of projection growth of population trends suggests that t years from…

A: Population of certain community as a function of years “t” is given as follows:P(t) = -t3 + 9t2 +…

Q: In a particular very small region, the consumer price index, C, depends on the current value of…

A:

Q: The city of Anville is currently home to 29000 people, and the population has been growing at a…

A:

Q: A bacterial colony is rapidly expanding. It has 10 bacteria at time t=0 and 2000 bacteria at time…

A: As per our guidelines we only solve first question and rest of the question will be reposted.

Q: Two tanks are connected as in Figure Q2b. Tank 1 initially contains 20 kilograms of salt dissolved…

A: Here we will use differential equation to solve this problem

Q: Consider a competitive market in which price adjusts to excess demand or supply and firms enter and…

A: given that                                                 dpdt=0.5qD-qs where qD is demand…

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

A:

Q: In a room containing of air 20,000 m3 of air, 600 m3 of fresh air flows in per minute, and the…

A:

Q: b) Let at time t years, an industry consumes fuel at the rate of (2t + 9) million barrels per year.…

A: Given an industry consumes fuel at the rate of 2t+912 million barrels per year. If the total supply…

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.