8. Polonium-210 has a half-life of 140 days. Suppose a sample of this substance has a mass of 300 mg. a) Find a function that models the amount of the sample remaining at time t.

Q: 2-The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at…

A: image is attached

Q: 24. Suppose that the half-life of Plutonium is 24000 years. a) Find a function P(t) that models the…

A:

Q: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

A: suppose that 50,000 bacteria are in a dish and that the population decays continuously by 4% per…

Q: d) A population of 100 bacteria decays at a rate of 5% each day How many bacteria, y, will there be…

A:

Q: When time is measured in​ days, the decay constant for a particular radioactive isotope is 0.16.…

A: The equation for radioactive decay is N(t)=N0(e-λt), where N(t) is the new amount of isotope , N0is…

Q: 5. Consider a scenario in which a 20ft tall lamppost lights up a street. A 5ft tall woman stands…

A: GIVEN: Height of tall lamppost lights = 20 ft

Q: The population in California p(t) (in million) can be approximated by the logistic growth function…

A:

Q: .

A: We will find the temperature.

Q: A recent report by the U.S. Cen- sus Bureau predicts that the U.S. Hispanic population will increase…

A:

Q: Suppose the function f has an initial value of 1,000 and a decay rate of 5%. Let the function g have…

A: Solution: we know that The equation of an exponential decay function is given by where a = initial…

Q: 2. The population of a town grows at a rate proportional to the population present at time t. The…

A:

Q: 3. A process creates a radioactive substance at the rate of 1 g/hr, and the substance decays at an…

A: 3. Rate of creation of radioactive substance is 1 g/hr The mass of substance at time t is q(t) gm…

Q: A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial…

A:

Q: If population y grows at a rate proportional to the current population, then y could be

A: This make separable differential equation

Q: 2. The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at…

A:

Q: The natural law of decay is used to study the radioactive decay of Radium: dm -km dt Where m is the…

A:

Q: Suppose that dP/dt = 0.19P(t) represents a mathematical model for the growth of a certain cell…

A:

Q: A sample of 500 g of radioactive lead-210 decays to polonium-210 according to (c) 10 yr. (d) Find…

A:

Q: 4. Suppose that the marginal propensity to consume is dc 0.7-ey (in billions of dollars) dy and that…

A:

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

A: This question is based on exponential decay.

Q: 11. Show that if positive functions f(x) and g(x) grow at the same rate as x→∞, then f = 0(g) and g…

A:

Q: Suppose the following graph represents the number of bacteria in a culture t hours after the start…

A: Answer is mentioned below As per the guidelines we are suppose to answer only first 3 subparts.…

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

Q: 4. The population of Lalaland is 600,000 currently and is expected to grow (continuously) at 3.5%…

A: The present population P =600,000 Growth rate r = 3.5 % per year To find population after time t =…

Q: 2. The liquid base of an ice cream has an initial temperature of 210°F before it is placed in a…

A: Given : The liquid base of an ice cream has an initial temperature of    To find at what time will…

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: projected that, t months from now, the population of a certain town will be growing at the rate of…

A:

Q: Suppose that the number of bacteria in a culture at time t is given by N = 5000 (25 + te ). (a) Find…

A: Given that the bacteria culture model at a time t is given as  Nt=500025+te-t20 To find the largest…

Q: 2. a) A ladder 10 meters long is leaning against a vertical wall with its other end on the ground.…

A: a)

Q: At time t = 0, there is one individual alive in a certain population. A pure birth process then…

A: A pure birth process gives the successive birth times as 25.8, 42, 52, 55.8, 59.2, 63.3. The process…

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.…

Q: Suppose a certain population is initially absent from a certain area but begins migrating there at a…

A:

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A:

Q: When time is measured in days, the decay constant for a particular radioactive isotope is 0.14.…

A: The decay of an object follows the exponential model  where N(t)I is the amount remaining after time…

Q: 4. The population of a trading area is currently 100 thousand. At time t years from now population…

A:

Q: A bacterial population B is known to have a rate of growth proportional to B itself. If between noon…

A: Solved below

Q: A bacterial colony is rapidly expanding. It has 10 bacteria at time t=0 and 2000 bacteria at time…

A: As per our guidelines we only solve first question and rest of the question will be reposted.

Q: A certain radioactive isotope has a half-life of 5 days. If one is to make a table showing the…

A:

Q: A bacterial population B is known to have a growth rate proportional to B itself. If between 3pm and…

A:

Q: 1. A breeder reactor converts relatively stable uranium 238 into the isotope plu- tonium 239. After…

A: Here, A(t) is the amount of plutonium remaining at time t. So, we can create the I.V.P. dAdt=kA,…

Q: 2- An efficiency study of the moming shift at a certain factory indicates that an average worker who…

A:

Q: It is estimated that t months from now, the population of a certain town will be changing at the…

A:

Q: Suppose a population can be modeled by 50 P(t) = where time is in years since 2005. (1+75e--5t)…

A:

Q: 8. Determine the half-life of the substance if an initial 150mg has decayed to 50mg in a an of 20…

A: Given query is to find half life and the time when 95% amount decayed.

Q: 2- An efficiency study of the morning shift at a certain factory indicates that an average worker…

A: Given relation is: Qt=-t3+6t2+24t a). The worker's rate of production at 11 AM: So put t=3 in given…

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 the following graph represents the number of bacteria in a culture t hours after the start…

A:

Q: A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial…

A: please comment if you need clarification. if you find my answer useful put thumbs up. Thank you.

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.