Radioactive Decay The amount of radioactive isotope thorium-234 present in a certain sample at timet is given by A(t) = 500e-0.02828tgrams, where tyears is the time since the initial amount was measured. How long will it take for the amount of isotopeto equal 318 grams?

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Q: 14. Annual interest rate. Hardy Bank advertises that it com- pounds interest continuously and that…

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A: Concept: Let z represent the amount of salt in the tank at time t, where t is given in minutes…

Q: A tank contains 200 liters of fluid in which 30 grams of salt have been dissolved. A brine…

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

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Q: A tank contains 180 liters of fluid in which 10 grams of salt is dissolved. Brine containing 1 gram…

A: Let the amount of salt in grams at time t be A(t)We have given the initial amount of salt in grams…

Q: A tank contains 420 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram…

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Q: A tank contains 200 liters of fluid in which 10 grams of salt is dissolved. Pure water is then…

A: Introduction: A differential equation is one in which at least one unknown function's derivative,…

Q: In the tank of 100 liters of brine containing 50kg totally dissolved salt. Pure water is allowed to…

A: Let y(t) be the amount of salt dissolved in the tank in kilograms after t minutes. Initially amount…

Q: 2. Brine containing 3 lbs./gal of salt enters a large tank at the rate of 2 gals/minute and the…

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Q: A tank is initially filled to the brim with 1500 L of pure water. Brine containing 0.35 kg of salt…

A: !st we will make differential equation for amount of salt the will solve it to get total amount of…

Q: An investment has been making money. Its value has been increasing at the rate of 7.1% per year.…

A: Note: It is assumed that the interest is simple interest.   When the interest is simple, then the…

Q: 2. Bacteria grow in a nutrient solution at a rate proportional to the amount present. Initially,…

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Q: Bacteria grow in culture at a rate proportional to the amount present. Initially, 300 strands of the…

A: We can assume that the bacteria grow exponentially. The exponential growth rate can be expressed as…

Q: 6. A tank contains 40 liters of a chemical solution prepared by dissolving 80 g of a soluble…

A: Given:      Since initially there are 40 l of solution prepared by 80 g of substance. So, V0=40…

Q: A tank contains 80 kg of salt and 2000 L of water. A solution of a concentration 0.02 kg of salt per…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: A five-gallon bucket is full of pure water. Suppose we begin by dumping salt into the bucket at a…

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Q: The rate of disintegration of a radioactive substance is proportional to the amount of the substance…

A: Given that the rate of disintegration of a radioactive substance is proportional to the amount of…

Q: Find the t-interval of interest and how much sugar is in the container after 25 minutes.

A: Given:

Q: 32. An experiment starts and the population of a bacteria culture increases by 10% in the first…

A: According to the question, experiment starts and the population of bacteria culture increases by 10%…

Q: Supercavitation is a propulsion technology for undersea vehicles that can greatly increase their…

A: HERE PERFORM ONE SAMPLE Z-TEST

Q: A tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 1 gram…

A:

Q: A tank contains 50 kg of salt and 2000 L of water. A solution of a concentration 0.0125 kg of salt…

A: Given: The tank contains 50 kg of salt and 2000 L of water. A solution of concentration 0.0125 kg of…

Q: A tank contains 150 liters of fluid in which 20 grams of salt is dissolved. Brine containing 1 gram…

A:

Q: cistern contains 50 gallons of brine with 10 pounds of salt. Another brine solution containing 2…

A: To calculate the amount of salt in the cistern after t minutes.

Q: 5. Consider a tank used in certain hydrodynamic experiments. After one experiment the tank contains…

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Q: Radioactive Carbon-14 The percentage P of radio- active carbon-14 remaining in a fossil after t…

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Q: 3) A hot pie is just taken out from an oven with a set temperature of 175°F. It is placed near a…

A: We know that , 20 °C = 68° F

Q: A tank contains 200 liters of fresh water. Brine containing 2 kg/liter of salt enters the tank at…

A: Let the amount of salt be Q. Volume at any time t: 200+4-3t=200+t The concentration becomes Q200+t.…

Q: A tank contains 100 kg of salt and 1000 L of water. A solution of a concentration 0.05 kg of salt…

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Q: An investment has been losing money. Its value has been decreasing at the rate of 13.1% per year.…

A: We have to use compounding series formula.

Q: A population of a particular yeast cell develops with a constant relative growth rate of 0.4393 per…

A: Population Growth of yeast cell: P(t)= Poeλt

Q: A tank contains 60 kg of salt and  1000 L of water. A solution of a concentration 0.03 kg of salt…

A: Question is solved.

Q: A 2000 L tank initially contains 40 kg of salt dissolved in 1000 L of water. A brine solution…

A: Consider the amount of salt in 1000L water as xt. Initially x0=40. Rate of change of salt is inflow…

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Q: A tank contains 300 liters of fluid in which 50 grams of salt is dissolved. Brine containing 1 gram…

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Q: 13) Population: Radioactive waste is leaking out of cement storage vessels at the rate of te02…

A: The rate of radioactive waste leaking is  te0.2t hundred gallons per month. We have to find the…

Q: A 40mg sample of a radioactive isotope decays to 30mg in 6.0 hours.  Determine its half life, to 2…

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Q: The initial population size of rock ptarmigans in an area is 500 ptarmigans. The growth rate is 0.2…

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Q: 750,000 + 0.55x 18) The average cost per unit, y, of producing x units of a product is modeled by y…

A: question 18 is based on inequality and linear programing. Attaching photo of solution.

Q: A tank contains 200L of a dye solution with a concentration of 1gram per liter. To prepare for the…

A: A tank contains 200L of a dye solution with a concentration of 1gram per liter. To prepare for the…

Q: radioactivity of an element decreases by 72 percent in 820 days. Determine the half-life of the…

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Q: ] = concentration of react= , = initial concentration o: * = rate constant t = time

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Q: U.S. Population Using data for selected years from1990 and projected to 2050, the total U.S.…

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Q: A tank contains 7070 kg of salt and 10001000 L of water. A solution of a concentration 0.035 kg of…

A: Given: The concentration of salt in 1000 L water is 70 Kg. The rate at which the 0.035 Kg of…

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.