A yeast grows at a rate proportional to its present size. If the original amount doubles in two hours, in how many hours will it triple?

Q: suppose the population of a certain bacteria in a laboratory sample is 100. if it is doubles in…

A: Given: The population of a certain bacteria in a laboratory sample is 100 and it is doubles in…

Q: If a town has a population of 850 people at year t=0, what is the formula for if it grows at a…

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Q: A radioactive substance decays at a rate proportional to the amount present, and half the original…

A: given radioactive substance that its half life is 1500 years. we have to find time after which the…

Q: A bank pays interest at a rate of 5%. What is the yearly multiplier if interest is compounded (a)…

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Q: A population of rabbits grew from 10 to 3000 in 24 months. Determine the doubling rate.

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Q: 4. If the population of a country doubles in 50 years, in how many years will it triple under the…

A: Solve the given for the timing of triple population

Q: If the population of the earth was found to be 3.5 billion in 1970, and Is Increasing at a rate of…

A: The population of the earth was 3.5 billion in 1970,  We are to find at what year population of…

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: 25. A 10-foot ladder is placed against a vertical wall. Suppose that the bottom of the ladder slides…

A: Given :-  dx/dt= 3feet/sec  Ladder height= 10feet  Find rate at which ladder is sliding down from…

Q: There are currently 100 cells in a culture and it grows at a rate proportional to its size. After…

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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: A radioactive substance has a half-life of 64 hours. If 200 grams of the substance are initially…

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Q: 1. The population of a community is known to increase at a rate proportional to the number of people…

A: Topic:- exponential function

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

A: Given that , The radioactive material is known to decay at a rate proportional to the amount…

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Suppose…

A: I have appended the formula used in the solution part.

Q: if water rises 1/2 inch in 3/7 of a week in a water reservoir, at what rate is the water rising per…

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Q: Radium decomposes at a rate proportional to the quantity present. If at the end of 20 years…

A: Solution

Q: at a rate proportional to the current population, and in the absence of other factors, the…

A: Consider at time t the population of mosquitoes is N in the area

Q: Water is pumped from a tank at constant rate, and no more water enters the tank. If the tank…

A: Given: The amount of water at 3:56 PM is 10452 L and amount of water at 4:12 PM on same day  is 8092…

Q: 3. Radium decomposes at a rate proportional to the amount at any instant. In 100 years, 100 mg of…

A: Given: initial mass of Radium  y0=96 mgWe know that General decay equation is y=y0e-kt…

Q: There are 5,000 wolves in the park, but their population is expected to decay at a rate of 8% per…

A: Given, initially , wolves in the park = 5000 Decay of population = 8% per year finally , wolves in…

Q: If a piece of machinery depreciates continuously at an annual rate of 4%, how many years will it…

A: To find: The number of years it will take for the value of machinery to halve. Concept used: The…

Q: 4. In a culture of yeast, the amount of active ferment grows at a rate proportional to the amount…

A: Let's work on the problem straight from the statement "the amount doubles in 1 hour": let the…

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

A:

Q: An isotope of cesium has a half life of 29 years. If 1300 grams of cesium disintegrates over a…

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Q: A certain radioactive material loses mass at a rate proportional to the mass present. If the…

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Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

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

A:

Q: A tank contains 1,000 gal of brine in which 500 lb of salt are dissolved. Fresh water runs into the…

A: Form the first order differential equation and solve using separation of variables.

Q: If the population of a small city is 45,000. If the population grows at a rate of 3% per year, in…

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Q: A hypothetical cube grows at a rate of 64 m³/min. How fast are the sides of the cube increasing when…

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Q: Assume that the population of a certain city increases at a rate proportional to the number of…

A: Note: There are two problems of same type. We will solve the first one for you. Kindly repost the…

Q: A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present…

A: It is given that,a radioactive substance has a decay rate of 4% per hour. If 1000 grams of the…

Q: A wet towel hung from a clothesline to dry loses moisture through evap-oration at a rate…

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Q: There are 100 bacteria cells in a dish now, but in 5 hours there will be 147 cells. At what rate do…

A: There are 100 bacteria at initial time t=0. In 5 hours that is when t=5, there will be 147 cells. In…

Q: 3. If a radioactive substance is quickly decaying at a rate of 13% per hour approximately how much…

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Q: A certain population of bacteria doubled after 20 minutes. If it is known that it grows proportional…

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Q: The population of one state increases at a rate numerically equal to the cube root of the…

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Q: A radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of radium…

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Q: A bunch of hooligans dump 164 pounds of  pizza boxes into a lake. If the pizza boxes dissipates at a…

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

A:

Q: A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds…

A:

Q: In a chemical reaction, a certain compound changes into another compound at a rate proportional to…

A: Let y be the unconverted amount of substance A at time t. Thus, the given information can be written…

Q: The population of an endangered species decreases at a rate of 7% per year. Approximately how long…

A: Answer

Q: In the 2000 U.S. Census, a small city had a population of 50,000. By 2010, the population had…

A:

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

A: The decay rate is proportional to the amount present. So, dNdt=-λN⇒dNN=-λdt⇒∫dNN=-λ∫dt+C⇒ln…

Q: A certain mold grows at a rate proportional to its present size. If the original amount doubles in…

A: Given that a certain mold grows at a rate proportional to its present size. And the original amount…

Q: The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time…

A: Given- Half life t12 =3.3 hours, Intial weight=1 gm. To find- The time in which the radioactive…

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.