In a chemical reaction a substance decomposes at a rate proportional to the amount of substance present. If half the initial amount of the substance remains after 20 minutes, and 8 grams remain after 100 minutes, how much of the substance was initially present?

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

A:

Q: The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: Given that rate of decay of radium is proportional to the amount present at that time.

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 radioactive material decays at a rate proportional to its amount. If the material has a life of 30…

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

Q: 2. In a certain bacterial culture where the rate of growth of bacteria is proportional to the number…

A: Solution is given below:

Q: The rate growth of a population is proportional to the present population. If it is 1000 initially…

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

Q: The population of a state is known to grow at a rate proportional to the number of people presently…

A: Follow the steps.

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

A:

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

A:

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

A: Solution

Q: This year there were 3,000 new births in a county, but new births are expected to grow at a rate of…

A: This year there were 3,000 new births in a county, but new births are expected to grow at a rate of…

Q: A population of bacteria grows at a rate proportional to the number of bacteria at the time. There…

A: Given that:                      Bacteria growth rate is proportional to the number of bacteria at…

Q: The half-life of a radioactive substance refers to the amount of time it will take for the quantity…

A: Given that: Half life of Q is: T=20 years In 2015 Initial amount: N0=100 g a). How much will be at…

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: A radioactive material decomposes half of its amount per minute. If after 2 mins, 100% undecayed…

A:

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

A:

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

A:

Q: The rate at which the body cools is proportional to the difference in temperature of the body and…

A:

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

A:

Q: Bacteria grown in a certain culture increase at a rate proportional to the amount present. If there…

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

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

A: In a certain culture of bacteria, the rate of increase is proportional to the number present. We…

Q: The substance decomposed at a rate proportional to the amount resent. What is the half-life of the…

A:

Q: In a certain bacteria culture the rate of increase in a number of bacteria is proportional to the…

A: Follow the steps below to solve a differential equation(in terms of x and y) by the variable…

Q: The half-life of a substance is 24 hours. About how many hours will it take for 6 grams to decay to…

A: SOLUTION

Q: The population of Tagum City is increasing at the rate proportional to its current population. In…

A:

Q: If the tank is completely full, how much is overflowing if 530 GPM is being taken off the bott

A: Given: Let the rate of filling be Qin = 1250 GPM  the rate of draining be Qdrain = 530 GPM Because…

Q: The population of a district in a town is known to increase at a rate proportional to the number of…

A: We will find out the required initial population of the state .

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

A: Solution

Q: Radium decomposes at a rate proportional to its present radioactive. In 100 years, 100 units of…

A:

Q: Radium decomposes at a rate proportional to the amount present. If 100 milligrams of Radium at…

A:

Q: A piece of machinery valued at $30,000 depreciates at a rate of 10% yearly. How long will it take…

A:

Q: The rate of decay of radium is said to be proportional to the amount of radium present. If the…

A:

Q: The growth rate of a certain strain of bacteria is unknown, but assumed to be constant. When an…

A: Given that the bacteria is growing at a constant rate. Initially there were 1500 bacteria and after…

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

A:

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: 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: 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: A radioactive substance has a half-life of 25 years. If 640 grams of the substance are present…

A:

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

A: Answer

Q: In one experimental study, the growth of a certain insects is increasing at a rate proportional to…

A: Given: The growth of insects is increasing at a rate proportional to the number present. To Find:…

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

A: Initial radium quantity Ni = 100 mg after t = 100 years N = 96 mg

Q: A certain population of rabbits grows proportionally to its size. If initially there are 1000…

A:

Q: A radioactive substance has a half-life of 4 hours. How much of it is left after 12 hours?

A: Since, a radioactive substance has a half-life of 4 hours.Our aim is to calculate the amount of…

Q: The number of germs in a certain culture increases at a rate proportional to the number present. If…

A:

Q: In a chemical reaction, substance A decomposes at a rate proportional to the amount of A present. It…

A: This decomposition reaction of first order, because rate is directly proportional to the…

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: A puppy weighs 2.0 lb at birth and 3.5 lb 2 months later. If the weight of the puppy during its…

A:

Q: 2. The population of a country doubles in 50 years. How many years will be 5 times as much? Assume…

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.