Suppose a population can be modeled by 50 P(t) = where time is in years since 2005. (1+75e--5t) During what year is this population growing most rapidly?

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A: Given: Let the rate of pumping in, Rin = 5 L / min Let the rate of pumping out, Rout = 4 L / min

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A: The Given Differential equation is: dPdt = 1.005P1-P7500

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Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A: GIVEN: Height of tall lamppost lights = 20 ft

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

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A: Use the Newton's formula for finding the time. First use the Newton's formula for finding k then…

Q: If f10,500 is invested fie 3 4ears at a rate of 9%.how much willyou have if interest Es compounded…

A: P=10500t=3 years.r=9%=0.09To find 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: The population of the world in 2015 was 9.75 billion people and was growing at a rate of 1.25% per…

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

Q: Suppose we have two 1 metre long rods. Each rod has a temperature of 0° on its left end with the…

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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$) P2'(t) = 140e0.07t (1000$)

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

A: This make separable differential equation

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

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Q: Lake Taal has a volume of 458 cubic km, and its rate of inflow and outflov are both 175 cubic…

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Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. (a) her shadow on the…

A: Given query is to y find the rate of change of length of the shadow.

Q: 5. Consider the problem: A water bucket is being filled with water from a water faucet at a constant…

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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

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

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Q: 4. The population of Lalaland is 600,000 currently and is expected to grow (continuously) at 3.5%…

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Q: City A has a current population of 500,00 people and grows at a rate of 3%/year. City B has a…

A: Given  City A :-  current population(P) is  500,00 people and growth rate (r) is 3% or 0.03  City B…

Q: 2. The liquid base of an ice cream has an initial temperature of 210°F before it is placed in a…

A: Given : The liquid base of an ice cream has an initial temperature of    To find at what time will…

Q: Suppose a population can be modeled by P(t) = %3D 200(1.052)*, where P(t) is in thousands and time…

A: Exponential function: - An exponential function in mathematics is one of the form f(x)=ax, where "x"…

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

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Q: Consider a scenario in which a 20ft tall lamppost lights up a street. (a) A 5ft tall woman stands…

A: Length is a measure of distance. In the International System of Quantities, length is a quantity…

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A: This question is related to population growth, We will solve it using integration.

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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: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

A: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

Q: 9. From 1975 to 2009, the age-adjusted incidence rate of invasive lung and bronchial cancer among…

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Q: A cylindrical tank holds 22 liters of water. At time t = 0, two taps are opened simultaneously, the…

A: Please check step 2 for the solution.

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

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Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

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Q: Find the linearization of ƒ(x) = log3 x at x = 3. Then round its coefficients to two decimal places.

A: Given: f(x)=log3(x) at x=3