() 18 where M, is the The half-life of a radioactive element can be modelled by M= Mo initial mass of the element, t is the elapsed time in hours, and M is the mass that remains after time t. The half-life of the element is 1100

Q: 1. A sum of $1000 is invested in a bank account that pays 10% compound interest monthly. The amount…

A: (a)Use the general formula for the compound interest to determine the values for k and a.…

Q: A quantity Q increases at a rate proportional to its current size. If the initial population is…

A:

Q: 9. The release of a fluorocarbons used in household sprays destroys the ozone layer in the upper…

A:

Q: 6. A chemist has a 20-mg sample of polonium-218. He needs exactly 81.5% of it for an experiment.…

A:

Q: (4) When interest is compounded continuously the amount of moncy S incrcases at a rate proportional…

A: See answer below

Q: (b) How much strontium-90 is left after 20 years" (c) When will only 100 grams of strontium-90 be…

A:

Q: 6. A colony of bacteria increases according to the law of uninhabited growth that is, N(t)= N,e".…

A: Given: Nt=Noekt

Q: 2. (a) (b) The weight of a radioactive substance remaining after t years is given by -0.04t W=1000x2…

A:

Q: 2. A bacterial population has an initial population of 1500. It is observed that the population is…

A: Initial population=1500 Population growth will be given by, P(t)=P0ektP0=1500

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

A:

Q: 4. Suppose that the variable P measures the population of bacteria in a Petri dish, and the variable…

A: The instantaneous rate of change of a function at a point is the slope of the curve of the function…

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

A:

Q: 10.) Let N represent a mass of carbon 14 (in grams), whose half-life is 5720 years. The quantity of…

A:

Q: 4) A culture initially has Po number of bacteria. At t =1 the number of bacteria is measured to be…

A: Given: A culture initially has P0 number of bacteria. At t=1, the number of bacteria is measured to…

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

A:

Q: 33. Early retirement. Lauren Johnson signs a 10-yr con- tract as a loan officer for a bank, at a…

A: Lauren has 3 years on her contract making $84,000 per year. With an interest rate of 4.7% the…

Q: 17. The decay of a certain substance is modelled by the function N(t) 100(3+e), where the number of…

A:

Q: 39. A population P, grows at the rate P'(t) = 5(t +1) In /t +1 %3D thousand individuals per year at…

A:

Q: 39. A population P, grows at the rate P'(t) = 5(t +1) In /t +1 thousand individuals per year at time…

A: Given population growth at time t  is  P't=5t+1lnt+1 Then…

Q: 4. Suppose that $5,000 is invested at 6.5% interest compounded daily. a. Determine the formula for…

A:

Q: A chemical reaction produces a desired chemical at a rate of r(t) = e-t grams per second at time t…

A: The rate of chemical reaction r(t)=e-t For the time interval 0≤t≤T Amount of chemical produced…

Q: 20. A certain bacteria is known to grow exponentially, with the population at time t given by the…

A:

Q: A population P of insects increases at a rate proportional to the current population. Suppose there…

A: In the given question we have to find the expression and population of insects after half year and…

Q: 3. How long will it take before twenty percent of our 1,000-gram sample of uranium- 235 has decayed?…

A: The life of Uranium 235 after 20 percent decay is t = 0.322 T where T is half life of U-235

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: 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: 8. Strontium-90 is a radioactive material that decays according to the function A(t) = Ane-0.0244t…

A: We will use given equation to find amount and time

Q: 3. Carbon 14 an isotope of carbon is radioactive and decays at a rate proportional to the amount…

A:

Q: of Let Q represent a mass radioactive plutonium (239pu) (in grams), whose half-life is 24,100. The…

A: The quantity of plutonium after t years is Q=1812t24,100

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

A: Given  The initial mass of a radioactive substance is m0 and the half-life of the substance is h.…

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: (3) Suppose we invested $20,000 at an annual rate of 5% where interest is compounded continuously.…

A: The main objective is to frame differential equation and solve them by using initial condition.

Q: 1. The price of a new machine is $14,000. After ten years, the machine has a salvage value of $750.…

A: Linear model  where, b = y intercept = starting value = $ 14,000

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: 2. Simple Chemical Conversion Radium decomposed at a rate proportional to the quality of radium…

A: Let's find time taken 1/2 the original amount of radium to decompose.

Q: The population of a certain species is given by N = 127 × 1.06t, where t is measured in years. What…

A:

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

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

Q: 21. Suppose the number of users for a new social media app increases according to y = Yoe0.1t where…

A:

Q: 10) The current in an electric circuit carries electrons past a certain point at the rate of 108- 12…

A: Given that the rate of electrons(e) per second(t) is

Q: Radium decomposed at a rate proportional to the quality of radium present. Suppose that it is found…

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: 8. A cup of coffee is originally 170°F at 3:00 when it is poured into a cup in a room that has a…

A:

Q: At the beginning of an experiment, a scientist has 352 grams of radioactive goo. After 225 minutes,…

A: Let the formula of G(t) is, Gt=G0e-kt

Q: 3. Boule's Law states that when a sample of gas is compresses at a constant temperature, the…

A:

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

A:

Q: 4.6.17 Find the half-life of a radioactive element, which decays according to the function The…

A:

Q: 1. A sum of $1000 is invested in a bank account that pays 10% compound interest monthly. The amount…

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