An initial amount of 100 g of the radioactive isotope thorium-234 decays according to Q(t) = 100e−0.02828t where t is in years. How long before half of the initial amount has disintegrated? This time is called the half-life of this isotope. (Round your answer to one decimal place.) t =____________________yr

Q: A breeder reactor converts uranium-238 into an isotope of plutonium-239 at a rate proportional to…

A: Given : Initial amount present is 190 pounds Remaining after 10 years is 0.9997 * 190 pounds we need…

Q: We invest a given amount of money in a bank account whose yearly rate is 3.5 %, compounded…

A:

Q: The number Nof bacteria present in a culture at time t (in hours) obeys the law of uninhibited…

A: Part (a) - Given equation -Nt = 1000e0.01tPutting t=0, to find number of bacteria at t=0.N(0) =…

Q: Adam is working in a lab testing bacteria populations. After starting out with a population of…

A: It is givne that the Initial population of the bacteria P0=411 and he observes the change in…

Q: The rabbit population at the city park increases by 5% per year. If there are intially 454 rabbits…

A: A)Population y in terms of y is given as;y(t) =P0 (1+r)t P0=454 r=0.05 y(t)=454 (1.05)t

Q: A principal P, invested at and compounded continuously, increases to an amount K times the oniginal…

A:

Q: The rabbit population at the city park increases by 11% per year. If there are intially 140 rabbits…

A: Given Let c be the initial rabbit population in a city. x be the year. r be the rate of population…

Q: The rabbit population at the city park increases by 3% per year. If there are intially 296 rabbits…

A:

Q: Radioactive iodine decay Radioactive iodine 131I is fre- quently used in tracer studies involving…

A: Solution: Consider the given formula for radioactive iodine decay is: A(t) = A0a-t where A0 is the…

Q: 1) THE POPULATION, P, OF A CERTAIN TOWN CAN BE MODELED BY THE EQUATION P = 2,005ekt, WHERE t = 0…

A: Given: The equation of population in the year 1990 is given as,  P=2005ekt where t=0. a) In 1975,…

Q: A sum of $900 at 8% interest compounded continuously will grow to V(t) = 900e.08t dollars in t…

A:

Q: The doubling period of a bacterial population is 10 minutes. At time t = population was 70000. 100…

A:

Q: When the population growth of a certain city was first studied, the population was 22 000. It was…

A: Given function for the population growth is P=22,000100.163t. a. Obtain the number of year that the…

Q: The rabbit population at the city park increases by 11% per year. If there are intially 114 rabbits…

A: Initial rabit population is 114, population increases 11% per year .we need to find an expression…

Q: The half-life of cesium-137 is 30 years. Suppose we have a 378-mg sample. Find the mass that remains…

A: Given data: The half-life of cesium-137 =30 years The general equation of decay is given as:…

Q: 19. The population of a small new community has 200 members and obeys the law of uninhibited growth…

A:

Q: Radon-222 The decay equation for a certain substance is known to be y = y0 e-0.0462t, with t in…

A:

Q: The rabbit population at the city park increases by 11% per year. If there are intially 311 rabbits…

A: Initially, there are 311 rabbits. Population increases 11% per year and that means 111% of the total…

Q: The motion of an particle follows an exponential function s(t)=et. (a) Determine the velocity of the…

A: If the distance function is differentiated with respect to the time, then the velocity function is…

Q: Erbium-165 decays at a rate proportional to the amount present. a) A lab technician has a 4-mg…

A: Given, initial a lab technician has 4-mg sample of erbium-165, after 10.4 hr, the sample reduced to…

Q: Californium-254 has a half-life of 61 days. A sample has a mass of 7O mg initially. I) What is the…

A: Given: Californium - 254 has a half life of 61 days. Initially it has a mass of 70 mg.

Q: ose that a large mixing tank initially holds 200 gallons of water in which 30 pounds of salt have…

A:

Q: y = yoe™ -1.61 The decay equation of a certain radioactive element is where t is measured in years.…

A:

Q: 5. Strontium-90 has a half-life of 28 days. A sample has an initial mass of 50 mg. a) Find an…

A: We use a model p(t) = m0ekt, Where p(t) is amount of mass remaining after t days.  m0 is initial…

Q: #13A and #13B

A:

Q: Decay Rate, k 6.7% per year = -0.067 Complete the table shown to the right for the half-life of a…

A: The table given is                                       Half-Life…

Q: A population of termites doubles every 0.35 days. The initial population is 1800 termites. a) How…

A:

Q: The doubling period of a bacterial population is 10 minutes. At time t population was 60000. 90…

A:

Q: An archaeological sample contains 0.622 g of lead-206 and 2.198 g of uranium-238. Assume that all…

A: Given that :- Mass of Lead=0.622g and Mass of Uranium=2.198g Decay rate for uraniumλ=1.54×10-10/year…

Q: 5) An isotope of lead decays according to the function remaining, in grams, after t minutes. a) What…

A:

Q: after 245 years half of a sample of a radioactive element remains. Find the constant k for this…

A:

Q: 2. A population of mosquitoes decreases exponentially. The size of the population, P , after t days…

A:

Q: A radio active material is to be used for an experiment. Its initial mass is x0 = 100 kg.. After 15…

A: Radioactive decay equation.

Q: A population of deer inside a park has a carrying capacity of 200 and a growth rate of 2%. If the…

A: topic- exponential function

Q: The half-life of cesium-137 is 30 years. Suppose we have 200 mg sample. How much of the sample…

A:

Q: 3. Given enough food and space, a colony of yeast increases at a rate proportional to its…

A:

Q: The doubling period of a bacterial population is 10 minutes. At time t = population was 90000. 80…

A:

Q: 4. Radium decomposes approximately at a rate proportional to the amount present. If it is 100 grams…

A: Given  at t=0, amount of radium = 100 grams and at t= 100 years, amount of radium = 96 grams.

Q: The rabbit population at the city park increases by 15% per year. If there are intially 258 rabbits…

A:

Q: f a quantity Q(t) exhibits an exponential decay and follows the rule Q(t) = 100e^−0.01t (a) Find the…

A: NOTE: Refresh your page if you can't see any equations. . here coefficient of t is -0.01 so the…

Q: A population of squirrels lives in a forest with a carrying capacity of 2300. Assume logistic growth…

A: According to the given information, logistic growth can be defined as the growth like S shape graph…

Q: 9. A particular compound decays according to the equation y = ae where t is in days. Find the…

A:

Q: 50 mg of radioactive substance decays by 20% in 10 years a. what is the value of k in the formula…

A: This is a question of differential equation. Based on the given data we will solve the all subparts…

Q: 10. The half-life of radium-226 is 1620 years. There is 100g of radium-226 in a particular sample…

A:

Q: An air-freshener starts with 33 grams and evaporates over time. In each of the following cases,…

A: We need to write formula for Q in each case and find change in B

Q: A population of mosquitoes decreases exponentially. The size of the population. P, after t days is…

A:

Q: 7.b

A:

Q: Strontium 90 decays at a constant rate of​ 2.44% per year.​ Therefore, the equation for the amount P…

A:

Q: A population of squirrels lives in a forest with a carrying capacity of 1700.  Assume logistic…

A:

Q: 22. The half-life of radium-226 is 1620 years. There is 100g of radium-226 in a particular sample…

A: Nr=No12rr2Nr=quantity of substance remainingNo=initial quantityr=rime flowr12=half life

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.