4.6.17 Find the half-life of a radioactive element, which decays according to the function The half-life of the element is -0.0377t A(t) = Age where t is the time in years. |years. (Round to the nearest tenth.)

Q: 17. Lance accidentally lets a spider into the IUPUI experimental nuclear reactor. If the spider…

A: Given function, W(t)=0.01e4.5t Where W(t) is the weight of the spider(in kilograms) after t days.

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

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Q: The amount of iodine 131 remaining in a sample that originally contained A grams is approximately…

A: The equation for the amount of iodine 131 remaining in a sample that originally contained A grams…

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Q: The half-life of a certain radioactive substance is 12 hours. There are 8 grams present initially.…

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Q: 5. The decay constant for a particular radioactive element is 0.015 when time is measured in years.…

A: Given: The deacy constant for a particular radioactive element is 0.015 when time is measured in…

Q: 3) A certain radioactive material loses mass at a rate proportional to the mass present. If the…

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Q: 2. The position of particle x (in meters) is a function of time t (in seconds) given by the formula…

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Q: If $3000 is invested at 6.7% compounded continuously, graph the amount in the account as a function…

A: $3000 is invested at 6.7% compounded continuously for 9 years. We have to find the amount. let us…

Q: 65. f(1) is the value after t years of a $1,000 investment depreciating continuously at an annual…

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Q: The number of bacteria in a certain sample increases according to the following function, where y,…

A: Given that, the number of bacteria in a certain sample increases according to the following function…

Q: Q1. A certain radioactive material is known to decay at a rate proportional to the amount present.…

A: Let x(t) be the amount of radioactive material which is present in milligrams after t years. Given…

Q: e) What are the domain and the range for this situation?

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Q: 5. A bacteria colony grow at a rate of 11% per year. If the initial sample has a mass of 500 gram…

A: Initial mass of the bacteria P0=500 grams  growth rate r=11% per year =0.11 per year  Let size of…

Q: Strontium-90 is a radioactive substance that decays according to the following function, where yo is…

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Q: Suppose that P = f(t) is the population (in millions) of the country t years after the year 2000.…

A: Given that P= f(t) is the population (in millions) of the country t years after the year 2000

Q: On every exponential curve y = 6 (b > 0,b # 1), there is exactly one point (ro, yo) at which the…

A: Given exponential curve is: y=bx To find equation of tangent, first find slope using calculus…

Q: suppose that the initial mass of a radioactive substance is m0 and the half-life of the substance is…

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Q: 6. A mine worker discovers an ore sample containing 500 mg of radioactive material. I vas discovered…

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

Q: Fit an exponential curve of the form y = ab* to the followin 1 3 4 6. 1.0 1.2 1.8 2.5 3.6 4.7

A: Introduction: The graphical method has the disadvantage that the straight line drawn may not be…

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

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Q: 8. Polonium-210 has a half-life of 140 days. Suppose a sample of this substance has a mass of 300…

A: Given that the half-life of Polonium-210 is 140 days And mass of a sample of this substance = 300 mg…

Q: 2. Suppose the remaining quantity, measured in grams, of a radioactive substance present after time,…

A: Given: Qt=500e-0.05t we know that at half life quantity of radioactive substance will be half of…

Q: 1 Find the exponential function f(x) = a* that passes through the point - 3, 216 and has a y- -…

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Q: Suppose that when a certain lake is stocked with fish, the birth and death rates B and 8 are both…

A: (a)

Q: Q1. A certain radioactive material is known to decay at a rate proportional to the amount present.…

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Q: #3 The population in a region can be approximated by the function P(t) = 325 + (t + 10)e-(t+10)/20…

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Q: 9. The half-life of a radioactive element can be modelled by M = Mo (-)" where Mo is the initial…

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: A certain radioactive substance has a half-life of 22 days. As a sample of the radioactive substance…

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Q: 2. Find an approximate equation y = ab* of the exponential curve that contains the given pair of…

A: The objective of the question is determine the approximate equation at given data.

Q: A radioactive substance decays according to the following function, where y, is the initial amount…

A: Given radio active substance decay is represented by following function,  y = y0 e-0.0645t  Where y0…

Q: Suppose that the time T (in days) for a cancerous tumor to double in volume (in cm) is given by…

A: The Given data are: The time is T=13ln2lnV1-lnV0V0<V1, the volume of the tumor is V0=22 cm3, and…

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: Astatine-210 is a radioactive substance that decays according to the following function, where  y0…

A: Given: y=y0e-0.086t       ........(1)

Q: 2. It has been observed that a mothball of radius 1 cm evaporates to leave a ball of radius 1/2 cm…

A: We will use rate of evaporation ( change in surface area ) is proportional to surface area formed a…

Q: 46. The following equation is used to calculate the aver- age firing rate f of a neuron (in spikes…

A: The equation fx=20e3x2.1+e3x is used to calculate the average firing rate f of a neuron (in spikes…

Q: A sample of 800 g of an isotope decays to another isotope according to the function A(t) = 800…

A: We have given sample of 800 g of an isotopes decays to  another isotopes according to the function…

Q: The amount of iodine 131 remaining in a sample that originally contained A grams is approximately…

A: Given that the amount of iodine 131 remaining in a sample in t days  is Ct=A0.9175t Where A grams…

Q: 6. The half-life of radium is 1690 years. (a) Compute the decay constant k ( 5 decimal places)

A: Given: The half-life of radian that is 1690 years. N0=10 g t=50 years

Q: 0s15 20, where i is the number of years after the base year of 1905. 20. During the time period…

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Q: The number of bacteria in a certain sample increases according to the following function, where y,…

A:

Q: The number of bacteria in a certain sample increases according to the following function, where y,…

A: The number of bacteria in a certain sample increasesy=y0e0.0264 t

Q: 8) Suppose that the number of bald eagles in the U.S. at any given time is given by P(t) = 50, 000 –…

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Q: trontium-90 is a radioactive isotope that can be produced using nuclear fission, and has a half-life…

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Q: 9. The following table shows data for the cost of natural gas in Maryland (in dollars per Million…

A: Hello, Thanks for posting your question here.  Since you have posted a question with multiple…

Q: 7. If the number of bees in a beehive are modeled by the function 6(t) = te +1 thousand bees, where…

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

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Q: 3. Given 100 grams of bacteria that decreases at a rate of 2 per year. What would be an appropriate…

A: Given:- Initial bacteria = 100grams               Rate of decrease = 1/2               Time.…

Q: 7. If the number of bees in a beehive are modeled by the function b(t) = te +1 thousand bees, where…

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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.