9. Sales for a speaker system have been growing at the rate: f'(t) = 2000(3 – 2e-t) systems/yr where t is the number of years they have been on the market. How many systems where sold in the 1$t 5 years?

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: 1) Assume that a tumour at a rate of G(1) = 13 mg/day at time t grows %3! days. What is the total…

A: integration

Q: A bacterial population is 7000 at time t = 0, and its rate of growth is 1,000 · 4t bacteria per hour…

A: It is given that at t=0 bacteria population is 7000   The growth rate is 1000*4t

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: Cane sugar, when placed in water, converts to dextrose at a rate proportional to the amount of…

A: An ordinary differential equation is an equation containing independent variables, dependent…

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: 2. The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: A(t) = amount remaining in t years          = A0ekt, where A0 is the initial amount and k is a…

Q: After ·t months, the production output at a certain factory is N (t) thousand units, where N (t) =…

A:

Q: A tank initially contains a solution of 10 pounds of salt in 60 gallons of water. Water with 1/2…

A:

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

A: Solve for the value

Q: a new substance C is to be formed by removing two units from each of two substances whose initial…

A: 1st we will formed a differential equation for amount of C and then solve it to get actual amount of…

Q: The yearly rate of consumption of natural gas (trillions of cubic feet) for a certain city is…

A:

Q: The growth of bacteria in food products makes it necessary to time-date some products (such as milk)…

A: Given, ƒ(t) = 500e0.1t  t- in days f(t)- in millions.

Q: 2 Consider the impact function of a certain drug, I = 0.25D/100 – D, with I a percentage and D in…

A: We will find out the required value.

Q: the number of U.S. Citizens aged 65 year and older from 1900 through 2050 is estimated to be growing…

A: Given: Rt=0.063t2-0.48t+3.87 As it is given that 0≥t≤15 Hence, t=0 for 1900 and t=10 for 2000 and…

Q: 3. A mixture is transferred into a cylindrical container through a conical filter. If the filter is…

A: The volume of a cone: V=13πr2h Where, r  is the radius of the cone. h is the vertical height of the…

Q: Consider and solve the initial value problem of a new form of life discovered on a distant planet.…

A:

Q: When air expands adiabatically (without gaining or losing heat), its pressure P C where C is a…

A:

Q: 1. A honeybee population starts with 100 bees and increases at a rate of f'(t) bees per week. What…

A:

Q: It is estimated that t years from now the population of a certain lakeside community will be…

A: The population is changing at the rate of 0.6t2+0.2t+0.5 thousand people per year. That is,…

Q: 2. The rate at which the number of bacteria in a culture is changing (in thousands of bacteria per…

A: As per our limit we can answer only the first question. If you want other questions to be answered…

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

A:

Q: Assume that in a certain country, the rate at which jobs are created is proportional to the number…

A: Explanation: Suppose that number of jobs  = N Here given that, the rate at which jobs are created is…

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

A: We will use the exponential growth equation of bacteria .

Q: 1. (a) If V is the volume of a cube with edge length x and the cube expands as time passes, find…

A: Topic = Derivative

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

A: The rate at which the height of the tree changes is given by,h'(t)=3t2+t    ft/yr…

Q: If the instantaneous growth rate of COVID19 is modeled by (limHh->0)(200t+100h). At t=5 seconds…

A:

Q: Show your working while calculating the instantaneous rate of increase (dN/dt) at 4 K and ¼K. Is it…

A: question:

Q: If the marginal revenue (in dollars per unit) for a month is given by MR = −0.2x + 250, what is the…

A: The marginal revenue (in dollars per units) for a month is given by-

Q: A certain population of microorganisms grows at a rate proportional to the amount present under a…

A: Given that, A certain population of microorganisms grows at a rate proportional to the amount…

Q: A point moves along the curve y = x ^ 3−3x + 5 so that x = 1/2√t + 3, where t is time. At what rate…

A: Given- y=x3-3x+5 and x=12t+3 To find- The rate of changing when t=4. Concept Used- dydt=dydx·dxdt

Q: [2] The rate of growth of the bacterial population is proportional to the number of bacteria present…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

A:

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A:

Q: The amount of radio active material present at time t is given by A=Aoe*t, where Ao is the initial…

A: As many Questions are given , I will solve only one: Let A0 be the initial amount. Given that 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: The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: 9. Suppose an object is moving along a path described by; f(t) = t - 6t, where f (t) is measured in…

A: The objects velocity at t is equal to 4 will be the objects instantaneous rate of change at that…

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: Suppose yy varies at a constant rate of change of -0.6 with respect to xx (so that…

A:

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

A:

Q: What is the result of integrating a population growth rate betweentimes t = a and t = b, where b…

A: Integrating a population growth rate between a to b that is ∫abRatedt

Q: Two substances, A and B, are being converted into a single compound C. In the laboratory it has been…

A:

Q: Consider a tank that initially contains 100 gallons of a solution in which 50 pounds of salt are…

A: Here I am attaching image so that you understand each and every step.

Q: If oil leaks from a tank at a rate of  r(t) gallons per minute attime t , what does ∫0120 r(t) dt…

A: Oil leaks from a tank at a rate of  r(t) gallons per minute at time t.

Q: Show that an investment that pays out R dollars per year continuously for T years has a PV of R(1…

A:

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A:

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

A: .

Q: A radioactive element decays according to the function Q=Q, e", where Q, is the amount of the…

A: We will solve the problem