Application of Integration A small town in South Africa has an annual population growth rate of e10* - - 2x people. If x represents number of years, then at x = 2 years, the population of the town was 1500 people. Souroo: fO 20311

Q: Population growth Growing from an initial population of 150,000 at a constant annual growth rate of…

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Q: A population of insects increases at a rate of 250 + 61 + 91? insects per day. Find the total insect…

A: let p(t) is represent population at t  Given dp/dt = 250+6t+9t² p(0) = 35 We have to find p(3)

Q: A dirty lake was contaminated by a toxic substance. The lake has a volume of 1.2M liters of water…

A: Here first we form the differential equation for the amount of toxic substance at time t as follows…

Q: Interest Rate Suppose that $30,000 is invested atcontinuous rate r and grows to $121,656 in 28…

A: Principle amount = $30000 Total amount grown at the end of 28 years= $121656 Amount of interest is…

Q: Annual sales of bottled water in a certain country in the period 2007-2014 could be approximated by…

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Q: A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt…

A: Given Initially tank contain 50 kg  salt And 2000 litre of water

Q: .A population of eight beavers has been introduced into a new wetlands area. Biologists estimate…

A: Solution:

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Q: A tank contains 90 kg of salt and 1000 L of water. A solution of a concentration 0.045 kg of salt…

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Q: Law of 70 Bankers use the law of 70, which says that if an ac- count increases at a fixed rate of…

A: Simple interest is calculated by multiplying principle amount with rate of interest and time divided…

Q: Logistic A Small lake Contains fish where the maximum length of this Kind of fish will not exced so…

A: Consider the given information: Initial length is 15 cm. Length after 4 weeks =30 cm. As the length…

Q: Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially, there…

A: growing of bacteria iss a exponential functiony=a(1+R100)t a. 800=250(1+R100)7 1+R100=1.18R=18% rate…

Q: 2. Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially,…

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Q: A bacterial population is known to have a rate of growth proportional to itself. A bacteria culture…

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Q: The temperature dependence of the equilibrium constant is given by the equation: ΔΗ In K = In A – RT…

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Q: A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt…

A: Given a tank contains 50kg of salt and 2000ltrs of watera solution of the concetration 0.0125kg of…

Q: After long study, tree scientists conclude that a eucalyptus tree will grow at the rate of 0.6 +…

A: Given that the rate at which eucalyptus tree grow per year is given as: 0.6+4t+13 feet per year,…

Q: A tank contains 60 kg of salt and 1000 L of water. Pure water enters a tank at the rate 8 L/min. The…

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Q: The amount of a radioactive isotope present in a certain sample at time t is given by A(t) = 400 e…

A: Solve

Q: Find the t-interval of interest and how much sugar is in the container after 25 minutes.

A: Given:

Q: Dating dinosaurs with potassium Dinosaur fossils are  often dated by using an element other than…

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Q: A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt…

A: Given: The tank contains 50 kg of salt and 2000 L of water. A solution of concentration 0.0125 kg of…

Q: A steel railroad rail expands and contracts according to the formula  Δl = αlΔT,  where Δl is the…

A: Calculate a steel rail road expands or contracts according to the formula ∆l=αl∆T where, ∆l is…

Q: cistern contains 50 gallons of brine with 10 pounds of salt. Another brine solution containing 2…

A: To calculate the amount of salt in the cistern after t minutes.

Q: 5. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains…

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Q: Draining a tank Water is drained from a 3000-gal tank at a rate that starts at 100 gal/hr and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: A bacteria culture starts with 300 bacteria and grows at a rate proportional to its size. After 5…

A: " Since you have posted a question with multiple subpart, we will solve first three subpart for you.…

Q: Radioactive Decay The amount of radioactive isotope thorium-234 present in a certain sample at timet…

A: Given :         The amount of isotope present in a certain sample at time t is            A(t) =…

Q: Radiometric dating Scientists can determine the age of  ancient objects by the method of radiometric…

A: Given: Half life of C14 is 5730 years. Percentage of remaining C14 in parchment is 74%. Let the…

Q: 3) A hot pie is just taken out from an oven with a set temperature of 175°F. It is placed near a…

A: We know that , 20 °C = 68° F

Q: A tank contains 100 kg of salt and 1000 L of water. A solution of a concentration 0.05 kg of salt…

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Q: A tank contains 100 kg of salt and 1000 L of water. A solution of a concentration 0.05 kg of salt…

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Q: Interest Rate Suppose that $20,000 is invested atcontinuous rate r and grows to $81,104 in 28…

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Q: The model P (t) = 720, 500 (1.088)" represents the population of a certain city since the year 1980.…

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Q: 2. A model that describes the population of a fishery in which harvesting takes place at a constant…

A: We need to solve DE.

Q: A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution…

A: Consider the amount of salt in 1000L water as xt. Initially x0=40. Rate of change of salt is inflow…

Q: 13) Population: Radioactive waste is leaking out of cement storage vessels at the rate of te02…

A: The rate of radioactive waste leaking is  te0.2t hundred gallons per month. We have to find the…

Q: . The barnacle falls off the wheel after 22.5 minutes. Use your regression  equation to predict the…

A: h(t) = 2.5 sin(2π/3(t-3/4)) + 2.0 or  h(t) = 2.5 sin[(t*2π/3)-π/2] + 2.0   Answer 1: h(22.5) =2.5…

Q: Use differentials to estimate the value of V1.4. Compare the answer to the exact value of V1.4.…

A: The given data is: Use the differentials to estimates the value of 1.44 And compare the answer with…

Q: tank contains 100 gal of fresh water.  A solution containing 5lb/gal of soluble lawn fertilizer runs…

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Q: The annual inventory cost C for a manufacturer is: C=1,008,000/Q + 6.3Q where Q is the order size…

A: Given:

Q: for every liter of water in a bucket there is initially dissolved 2 grams of salt. The bucket starts…

A: Consider the provided question, For every liter of water in a bucket there is initially dissolved 2…

Q: A factory installs new machinery that saves  S(x) = 1600 − 60x dollars per year, where x is the…

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Q: the population P (in millions) in Russian from 1996 to 2004 can be approximated by the model…

A: Given  P=152.26e-0.00039t

Q: A biotechnology investment, originally worth $30,000, grows continuously at the rate of 1,000e0.10t…

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Q: 3. Pollution Pollution from a factory is entering a lake. The rate of concentration of the pollutant…

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Q: At noon there were 500 litres of clean water in an outside swimming pool. At 1 pm it starts to rain,…

A: Let the amount of acid in the rain be x grams/Litre(g/L). Also, let y grams of acid is present after…

Q: Interest Rate Suppose that $10,000 is invested atcontinuous rate r and grows to $17,160 in 9…

A: Continuous return is given by formula R=Pert , where P is principal amount               R is…

Q: A tank contains 7070 kg of salt and 10001000 L of water. A solution of a concentration 0.035 kg of…

A: Given: The concentration of salt in 1000 L water is 70 Kg. The rate at which the 0.035 Kg of…

Q: Newton's law of cooling states that- = -k (x- A), where x(t) is the temperature of an object at dt…

A: according to newton's law of cooling  dxdt=-kx-A where xt is the temperature of an object at time t,…