Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy th

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A:

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: A radioactive substance is known to decay at a rate proportional to the amount present. In 2009…

A: Form a differential equation from the given problem to find solution.

Q: 6. The population of a community is known to increase at a rate proportional to the number of people…

A: We have to find the time it takes for the population to quadraple.

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

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

Q: a)How quickly is the water leaving the barrel over the first two seconds? b)Will the water drain…

A: The solution is given below in the next step:

Q: One type of lodine disintegrates continuously at a constant rate of 8.6% per day. Suppose the…

A: a. The model of the decay equation is given by P=P0ekt Here P0=10 grams of iodine         k = rate…

Q: The biomass of a yeast culture in an experiment is initially 29 grams. After 30 minutes the mass is…

A: Given: The biomass of a yeast culture in an experiment is initially 29 grams. After 30 minutes the…

Q: a). A drug in the blood stream decays by according to the equation y'=ky, where y is the…

A:

Q: Suppose that the fish population P(t)in a lake is attacked by a disease at time t=0, with the result…

A: From the given data, dPdt=βt-δtPβ=0δ=kPP0=100,000P20=1984Px=0x=?

Q: A certain population of bacteria grows such that its rate of change is always proportional to the…

A:

Q: 2. For a period of time, an island's population grows at a rate proportional to its population. If…

A: Let A0 be the initial population and k be the growth rate.A0 = 1174k = 6.5%  = 0.065

Q: The population of a certain municipality increases at the rate proportional to the present…

A: Here we solve the given population growth problem.

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Let initial population P0Population at time t is P.

Q: a city grows at a rate directly proportional to its population. The initial pop. is 30 and it…

A: The rate of change of the variable (Population here) is proportion to the variable itself. Hence,…

Q: The natural law of decay is used to study the radioactive decay of Radium: dm = -km dt Where m is…

A: This question is related to differential equations, we will solve it using given information.

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

A: This make separable differential equation

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

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Q: 3. The population of a certain country is known to increase at a rate proportional to the number of…

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Q: The natural law of decay is used to study the radioactive decay of Radium: dm -km dt Where m is the…

A:

Q: A colony of rats is transplanted into an island environment by stowing away on a cargoship. The…

A: Given that  A colony of rats is transplanted into an island environment by stowing away on a…

Q: 1. The heat index (HI) is an estimate of the temperature felt by the human body based on the actual…

A: Note: Here I am assuming T=107°F and rate=2°F Given: HI=-42+2T+10hr-0.22Thr-1.99T2hr2

Q: 1. If the growth rate of a culture of bacteria is proportional to the number of bacteria present.…

A: Given:  If the growth rate of a culture of bacteria is proportional to the number of bacteria…

Q: 5. The population of a community is known to increase at a rate proportional to the number of people…

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Q: 3. At time t, a certain radioactive material is known to decay at a rate proportional to the mass,…

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Q: According to one hypothesis, the growth rate dV/dt of a cell’s volume V is proportional to its…

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Q: 5) A cup of coffee cools at rate proportional to the difference between the constant room…

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Q: Radium decomposes at a rate proportional to the amount present. If the half-life is 1600 years, find…

A: NOTE: Refresh your page if you can't see any equations. . the initial amount is a=100% half-life is…

Q: a). A drug in the blood stream decays by according to the equation y'=ky, where y is the…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

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

A:

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

A: Let,Decay rate = r = -dAdt                        negative because it's decaying/decreasingwhere, r…

Q: Suppose a student carrying a flu virus returns to an isolated college campus of 1000 students. It is…

A:

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: 2. The population of the earth was 3 billion in 1970 and was increasing at a rate of 2% per year.…

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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: 4. One car leaves a given point and travels north at 30 mph. Another car leaves 1 hour later, and…

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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: Solve for bacteria after 20 hrs

Q: 3. The population of a community is known to increase at a rate proportional to the number of people…

A: Topic:-  exponential function

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

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

A:

Q: A mathematical model for population growth over short intervals is given by P=P0ert​, where P0 is…

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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: At time t years, an industry consumes fuel at the rate of (3t + 27)/3 million barrels per year. (i)…

A: Given that at time t years, an industry consumes fuel at the rate of 3t+2713 million barrels per…

Q: The state of decay of radium is proportional to the amount present at any time. Suppose that 400 mg…

A: Here we will find radium left after 2.5 hours and 10hours,

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A: Let x be the length, y be the width and z be the height of the box. The length is increasing at a…

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A: Introduction: In mathematics, a differential is an expression based on a function's derivative that…

Q: A certain gas satisfies the equation PV1.4 = C, where C is a constant, P is the pressure, and V is…

A: Given equation : P = 20 kg/cm2   V = 32  cm3dVdt=-2 cm3/min

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.