If f(t) = 1000e0.05sí represents the rate of flow of money for a vending machine over the first five years of income, then the total money flow for that time period is given by 1000e0.05t dt.

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

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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: Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the…

A: Let N(t) denotes the number bacteria present at time t. Use the proportionality constant k, to get…

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: The rate of growth of a population P is given by dP/dt=kP + N  where N is a constant representing…

A: Given:- The rate of growth of a population P is given by dP/dt=kP + N where N is a constant…

Q: A culture initially has P number of bacteria. At t = 3hour the number of bacteria is measured to be…

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

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Q: A study shows that if the government implemented energy conservation measures in 2009, the country's…

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Q: For any logistic equation, show that the point of inflection occurs at y = L/2 when the solution…

A: Given: The logistic equation

Q: A recent report by the U.S. Cen- sus Bureau predicts that the U.S. Hispanic population will increase…

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Q: In the equation, x² +y² = 45, what is the value of the rate of change in y with respect to time t…

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

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Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

Q: A population of insects increases at a rate of 260+6t+0.3t2 insects per day. Find the insect…

A: Rate of increase of population  of insects  dPdt = 260 + 6t + 0.3t2 per day

Q: 1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its…

A: Let the surface area be A So rate of evaporates is dA/dt, According to the question, dVdtαAdVdt=-kA…

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: If q'(t) is the growth rate of a population of a fish population in fish per month, what does…

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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: | Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V…

A: The given differential equation is dVdt=-140V, where V is the voltage and t is the time in seconds.…

Q: You invest some money in the stock market at time t = 0 months. If f(t), measured in dollars per…

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

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Q: a. A tank holds 1000 liters of water, in which 15 kg of salt is dissolved. Pure water enters the…

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1r dollars per…

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Q: It has been estimated that the total production of oil from a certain oil well is given by T(t) =…

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

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

A: Integral formula is ∫abf(x)dx=F(b)-F(a) ∫04n'(t)dt=n(4)-n(0) From the given integral…

Q: Determine the instantaneous rate of change of the function y = 5x + 2x² 1 with respect to x at x-4.…

A: Find instantaneous rate of change

Q: The rate of flow of a continuous income stream (in thousands of dollars per day) is given by f(t) =…

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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: 19. Suppose the rate of change of production of a regular worker at a factory is given by dp…

A: Given problem:- Suppose the rate of change of production of a regular worker at a factory is given…

Q: With U.S. Census Bureau data (actual and projected) for selected years from 1960 to 2050, the rate…

A: ∫xndx = xn+1n+1 + C, where 'C' is the constant of integration.

Q: 18. Estimate the instantancous rate of change of the function f(x) = x' +4x - 11x-30 at x = 1. Round…

A: Given,  f(x)=x3+4x2-11x-30, x=1

Q: What does r'(t)dt represent if r'(t) is the rate of growth of a dog in pounds for the t year?

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Q: A radioactive element decomposes at a rate proportional to the amount present. The amount remaining…

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Q: (b) If n'(t) is the growth rate of a bee population in bees per week, what does n'(t)dt represent?

A: Given,n'(t)=growth rate of bee populationt=time in weeks

Q: A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of…

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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: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: The half-life of a radioactive material whose rate of disintegration is proportional to the amount…

A: Given that, The half-life of a radioactive material whose rate of disintegration is proportional to…

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

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

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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: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: Find the PV of an income stream that pays out continuously at a rate R(t) = $5000e0.1t /year for 7…

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

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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…

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