The mass of a radioactive sample is given by M(t)=M010^-kt where t is the time in years, M0 is the initial mass and k is a constant if 400 grams of this material decays to 40 grams in 10 years what is the value of k?

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A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

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

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

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.…

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Q: A 200 g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138…

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Q: volume

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Q: A quantity with an initial value of 200 grows continuously at a rate of 55% per day. What is the…

A: Let the quantity Pn grown continuously at a rate of 55% per day. Initial quantity is P0=200.

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A: Let i = number of years = 0, 1, ... , 10 and the number of trees planting in the starting of each…

Q: A quantity with an initial value of 220 grows continuously at a rate of 9.5% per hour. What is the…

A: Consider the provided question, Given, initial value = 220  Rate, r = 9.5% = 0.095 per hour t = 225…

Q: The Chernobyl incident was the worst nuclear disaster in modern history. In 1986, a combination of a…

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Q: A 200 g sample of radioactive polonium-210 has a half-life of 138 days. This means that every 138…

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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: There are currently 250 cells in a culture and it grows ata rate proportional to its size. After one…

A: Given data: Total cells=250 After one hour=630

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.…

A: Rate of change

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Q: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: A quantity with an initial value of 200 grows continuously at a rate of 4% per second. What is the…

A: To find: The value of quantity after 1.55  minutes. Given: The initial value of quantity is 200 and…

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

A: We will solve the radioactive decay problem.

Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: Given: A radioactive element is known to decay at a rate proportional to its present mass.…

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A: Pressure and Volume are related by equation At a instant

Q: A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. What is the…

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Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

A: we have to determine time before the region is again habitable

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Q: Suppose the amount of oil pumped from one of canyon near the beach of island decreases at the…

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Q: 1. For a certain radioactive element decays at a rate of 37.7% per day (tis measured in days). How…

A: We need to find time.

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

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

Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

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Q: The half life of radium−226 is 1590 years. Let m(t) = m0 exp (kt) be the mass of radium−226 that…

A: Half time of the radium is 1590 years. m0=100mg Half time of the radium is 1590 years.…

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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: Initially 100 millions of radioactive substance was present. After 6 hours the mass has decreased by…

A: Given query is to find the amount of radioactive substance after 24 hours.

Q: A quantity with an initial value of 110 grows continuously at a rate of o.5% per hour. What is he…

A: Given, Initial value of quantity = 110  It is growing continuously at a rate of 0.5%  per hour.  We…

Q: Initially 87 grams of radioactive substance was present. After 3 hours the mass had decreased by 6%.…

A: We know that the differential equation of the decaydAdt=kAwhere A = amount and k = proportionality…

Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

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Q: It is projected that x years from now the population of a certain city will be changing at the rate…

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Q: The amount of decay of a certain radioactive element is given by -0.04t Yoe' where t equals time in…

A: The amount of decay of the radioactive element is given as follows. y=y0e-0.04t where t is the time…

Q: A radioactive element decays according to the function Q=Q, e", where Q, is the amount of the…

A: We will solve the problem

Q: Suppose a pollutant is seeping into the ground near a dump site at the rate of 2800 f(t) : (æ +…

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Q: A tank with a capacity of 25 L originally contains 15 L of brine with a concentration of 5 g/L of…

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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.