A radioactive element decomposes at a rate proportional to the amount present. The amount remaining after t years, AF, can be represented in the terms of the initial amount Ao where k is the negative constant of proportionality is

Q: If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A: This question is based on application of diffrential equation.

Q: The population of a certain community is known to increase at a rate proportional to the number of…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Here, initial mass =50 mg rate is proportional to the amount.m=50e-0.053t dmdtαm

Q: According to the Stefan-Boltzmann Law, the thermal radiation energy emitted (per unit time) by a hot…

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Q: A tank contains 300 gal of water and 100 gal of pollutants. Fresh water is pumped into the tank at…

A: Fresh water is pumped into the tank at the rate of 2 gal/min, and the well stirred mixtureleaves at…

Q: 2. Suppose that at some time t the mass of the tumor, M(t), is between 0 and K. What is the sign of…

A: We need to find sign of rate of change of M.

Q: The rate at which radioactive nuclei decay is proportional to the number of nuclei that are present…

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Q: It is known that the population of a certain country at time t is proportional to the people living…

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Q: When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of…

A: Consider the approximation cost of goods. Ct=p1.05t Rate of change of C=dCdt. So, Differentiate the…

Q: Assume that the rate of evaporation for water is proportional to the amount of water in a bowl. If…

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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: 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: If a quantity grows/decays at a rate proportional to its size, its growth can be expressed as dQ/dt…

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Q: 12. If a substance decomposes at a rate proportional to the amount of the substance present, and the…

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

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Q: The population of a certain country is known to increase at a rate proportional to the number of…

A: Consider the provided information, We assume that rate of change of amount of substance is…

Q: Tank A contains 274 litres of brine holding 123 N of dissolved salt, and tank B contains 274 litres…

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Q: 2. For a substance C, the time rate of comversion is proportional to the square of the amount x of…

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Q: (a) In a certain culture of bacteria the rate of increase is proportional to the number present. (i)…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

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Q: As part of the process in the production of a perfume, a certain substance with water is converted…

A: We have to formed a differential equation and solve it get amount converted or amount left

Q: nitially, there were 100 milligrams of a radioactive substance. After six hours, the mass decreased…

A: initially there are 100 milligrams of a radioactive substance. P=100 mg after 6 hour the mass…

Q: 12. If a substance decomposes at a rate proportional to the amount of the substance present, and the…

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Q: Radium decomposes at a rate proportional to the amount present at any instant. If initially there…

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Q: The initial mass of a certain species of fish is 3 million tons. The mass of fish, if left alone,…

A: Given problem Given that

Q: Suppose that an lowa class battleship has mass around 54,000 metric tons (54,000,000 kg) and a…

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

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: The volume (v) of a sphere varies directly with the cube of its radius (r). If k is the constant of…

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Q: 1. A tank contains 80 gallons (gal) of pure water. A brine solution with 2 Ib/gal of salt enters at…

A: Given that, a tank contains 80 gallons (gal) of pure water. A brine solution with 2 lb/gal of salt…

Q: If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A:

Q: The initial mass of a certain species of fish is 3 million tons. The mass of fish, if left alone,…

A: Solve the given problem

Q: A bacteria culture starts with a population of 1000 bacteria, and after 2 hours, the population grew…

A: Solution and Explanation is given below

Q: Tank A contains 402 litres of brine holding 123 N of dissolved salt, and tank B contains 402 litres…

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Q: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

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Q: Sugar dissolves in water at a rate proportional to the amount still undissolved. If there were 70 kg…

A: The amount of sugar present initially is 70 kg and at the end of 4 hours only 30 kg is left. The…

Q: A population of bees are dying at the rate proportional to the size of the initial hive, H(t), where…

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

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Q: Consider 250g of iodine which decomposes at a rate proportional to the amount present. Around 150g…

A: According to the company guidelines only first three 3 subparts will be answered in case of multiple…

Q: 2. For a substance D, the time rate of conversion is proportional to the square root of the amount x…

A: Given For a substance D, time rate of conversion is proportional to the square root of the amount x…

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

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

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: A tank contains 50 gallons of a solution composed of 90% water and 10% alcohol. A second solution…

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Q: Consider an animal population P(t) with constant death rate 8 = 0.01 (deaths per animal per month)…

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Q: 12. If a substance decomposes at a rate proportional to the amount of the substance present, and the…

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Q: The population of Normal, Illinois grows proportionally to its population at time t. At an initial…

A: Given, dPdt=kP Where P is the population and k is the proportionality constant.

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Image is attached with detailed solution.

Q: A radioactive material, such as one of the thorium isotopes, thorium-234, decays at a rate…

A: We will find the rate of decay as following.

Q: Tank A contains 407 litres of brine holding 181 N of dissolved salt, and tank B contains 407 litres…

A:

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.