2. Suppose the remaining quantity, measured in grams, of a radioactive substance present after time, t, is given by O(t) = 500eUst, where t is measured in days. a. Find the initial quantity present. b. Find the quantity present after a week. c. What is the half-life of the radioactive substance?

Q: Under laboratory conditions the half-life of ozone is approximately 25 hours. If Q =Q0ekt is the…

A: Given:- Under laboratory conditions the half-life of ozone is approximately 25 hours. If Q =Q0 ekt…

Q: The mass of a radioactive sample is given by M (t) = Mo10-k where t is the time in years, Mo is the…

A: Mt=M010-ktGiven that:M0=400 gM(t)=40 gt=10 yearsput all values in above equation and find 'k'

Q: 4. How much should be invested at 12.5% compounded continuously to end up with $1000 at the end of 5…

A:

Q: Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about…

A:

Q: If the initial mass of an Potassium was 159 grams will remain after 16 hours is 39.75 grams, then…

A:

Q: what is the​ half-life of a radioactive​ element, which decays according to the function…

A:

Q: A certain hermit wants to design a reactor using radioactive material A that will be converted into…

A:

Q: 17. The half-life of strontium-90 is 28 years. How long will it take a 50-mg sample to decay to a…

A:

Q: A sample of tritium-3 decayed to 94.5% of its originalamount after a year.(a) What is the half-life…

A: A sample of tritium-3 decayed to 94.5% of its original amount after a year. We have to find (a) What…

Q: 1. Radium decomposes at a rate proportional to the amount present. In 100 yrs, 100 mg of radium…

A: Given that Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg of…

Q: 1. A radioactive substance has a half-life of 1620 years. a. If its mass is now 4 g (grams), how…

A:

Q: A certain drug is eliminated from the bloodstream with a​ half-life of 34 hours. Suppose that a…

A:

Q: 9. If 75 mg of a radioactive substance decays to 15 mg in 20 years, find the Half-Life, in minutes,…

A:

Q: 2. Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

A:

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A:

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

A:

Q: Show that if a radioactive substance has a half-life of T, then the corresponding exponential decay…

A: For a substance with exponential decay the differential equation for the amount N  is dNdt=-kN. Here…

Q: 10. How long will it take you to reach $4000 compounded continuously if you invested the $5200 at…

A: A=$5200, P=$4000, r=4.7%=0.047

Q: If the initial mass of an Potassium was 183 grams will remain after 22 hours is 45.75 grams, then…

A:

Q: 11) Suppose that $4000 is invested at an interest rate of 5.8% per year, compounded continuously.…

A: We can find the answer for question-11 as below.

Q: How long does it take for 90% of a given quantity of the radioactive element cobalt-60 to decay,…

A: Radioactive element decay rate.

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

A:

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: 2-Suppose that the half-life of a certain radioactive substance is 2 days and there are 50g…

A: After each half life the amount left will be half the initial amount.

Q: _8. This refers to the initial amount of the growing quantity in the equation where the amount of t…

A:

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: Alice measures a radioactive sample at 1400 counts/minute on a Geiger counter. If the radioactive…

A: At initial the quantity of the substance is Ro = 1400 counts/minute.   At time t = 15 days   The…

Q: Following the birth of a child, a parent wants to make an initial investment P, that will grow to…

A: Given Initial amountP=P0 Interest rater=6%=0.06 Time t=18 years Future valueA=70,000

Q: In 1798 the English political economist Thomas R. Malthus claimed that, unchecked by environmental…

A: The growth rate can be evaluated as the change of the value of the function in the given time…

Q: A certain drug is eliminated from the bloodstream with a half-life of 34 hours. Suppose that a…

A: Exponential decay formula: - The amount drops gradually, followed by a quick decrease in the rate of…

Q: 4- The gross domestic product (GDP) of a certain country was N(t) = t² + 5t + 106 billion dollars t…

A:

Q: If the half-life of a radioactive substance is 6,700 years, then at what rate is it decaying? 1…

A: The decay law is given by, A(t)=A0e-kt Where, A0 is the amount at t=0. And, t1/2=ln2k

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: A company is considering expanding their production capabilities with a new machine that costs…

A: Cost of new machine = 53,000 Investment = 53000 Rate of interest, r= 0.7% per year = 0.007 Time = 9…

Q: Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000…

A: Given that the half life is 1000 years. This means 1/2 of the the original amount is left after 1000…

Q: An initial amount of 100 g of the radioactive isotope thorium-234 decays according to Q(t) =…

A:

Q: () 18 where M, is the The half-life of a radioactive element can be modelled by M= Mo initial mass…

A: The half-life formula is N=N012tt12. Here, N is the quantity remaining after time t, N0 is the…

Q: 3. What will happen to Joshua's money if his money will be 6.33% compounded continuously for 17.36…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 22. The half-life of radium-226 is 1620 years. a) If the current mass of a sample is 100 grams, what…

A:

Q: If the initial mass of an Potassium was 121 grams will remain after 22 hours is 30.25 grams, then…

A:

Q: The half-life of Carbon-14 is 7 years. How much of an initial 169 g sample will remain after 28…

A:

Q: 2. At what rate of interest, compounded continuously will an investment double in six years? 3.…

A: (2) given that the principle amount will gets doubled in six years if the amount is compounded…

Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

A:

Q: 9. A sample of tritium-3 decayed to 94.5% of its original amount after a year (a) What is the…

A: Consider N (t) is the amount of tritium-3 relative to the original amount, then general form is,

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: 12. The half-life of strontium-135 is 2 years, and its mass. A. is modelled by, where A, is the…

A:

Q: Assume a quantity decreases by 5.1% in 7.5 hours.What is the half-life of the substance?

A: Given:A quantity decreases by 5.1% in 7.5 hours.

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.