3. Radioactive carbon-14 fossil decays at a rate proportional to its amount present and has a half-life of approximately 5,700 yrs. Estimate the age of a fossil in which 80% of its carbon-14 has decayed?

Q: Determine whether the following statement is true or false, and explain why. The half-life of a…

A:

Q: 4. Radium decomposes at a rate proportional to the amount present. If half the original amount…

A: Solve differential equation

Q: 7. Traces of burned wood along with ancient stone tools in an archeological dig in Chile were found…

A:

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

A:

Q: A fragment of bone is discovered to contain 20% of the usual 14C concentration. Estimate the age of…

A:

Q: 2. A certain plutonium isotope decays at a rate proportional to the amount present. Approximately…

A: Let  at time t the amount of plutonium is  A(t)

Q: 6. The radioactive isotope of lead, PB-209, decays at a rate proportional to the amount present at…

A: Let's find time to take 90% of the lead to decay.

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: The half-life of Uranium-238 is approximately 4.5(10°) years. How much of a 10 kilogram block of U–…

A:

Q: 1. A sample of einsteinium-252 decayed to 64.3% of its original mass after 300 days. a) What is the…

A: Let 100 be the original mass 64.3% of 100 is  64.3100 of 10064.3100·100=64.3 Now we find out decay…

Q: If the half-life of a radioactive substance is 7,600 years, then at what rate is it decaying? 1…

A: We can find the rate of decay as below.

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

A:

Q: A sample of radium metal has a weight of 1.5 mg and a half-life of approximately 6 years

A: sample of radium metal has a weight of 1.5 mg and a half-life of approximately 6 years

Q: Of an initial amount of 9000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A: Apply the formula  P(t)=Po(1-r)t where, Po is the initial quantity r is the rate and t is the time.…

Q: Determine the equivalent effective rate of a money compounded continuously at r=5%.

A:

Q: If we are modeling a herd of clk, with an initial population of 100, in a region with a carrying…

A: Given that The population of elk satisfies a logistic growth model and  Initial population = 100…

Q: What is the characteristic growth rate of a population that is currently growing at a rate of…

A: simple growth rate formula will be used to solve the question.

Q: A scientist wants to determine the halflife of a certain radioactive substance. She determines that…

A: The half life function is given by: N(t)=N0(0.5)t/t1/2 where N(t) is the final amount in milligrams…

Q: 8) A bacterial culture has an initial population of 10,000. If its population declines to 3000 in 8…

A: Exponential model of population is given by,     P(t) = Po * e^(kt).

Q: Consider a population that begins growing exponentially at a base rate of 4.1​% per year and then…

A: Given that a population is begins growing exponentially at a base rate of  r=4.1% per year and then…

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

A: let amount of material present at any time t be p(t) let p0 be the intial  amount of material at…

Q: 7. A radioactive material decays at a rate proportional to its amount. If the material has a…

A:

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

A:

Q: If 275 mg of a radioactive element decays to 200 mg in 48 hours, what is its half-life?

A:

Q: 3. If a radioactive substance is quickly decaying at a rate of 13% per hour approximately how much…

A:

Q: 6. Determine the initial amount of radioactive substance if after 22 years, the remaining…

A: To find the initial amount of radioactive substance, decay rate and half-life of the substance.

Q: A radioactive substance has a half life of 175 years. Find the decay constant, r, for this…

A: A radioactive substance has a half life of 175 years

Q: If the half-life of a radioactive substance is 6,800 years, then at what rate is it decaying? (Hint:…

A:

Q: 10 - What is the total amount of 4200 TL with 3,8 % continuously compound interest after 4 years? a)…

A: Given that,initial principal amount,P=4200 Rate of interest,i=0.038 Number of years of deposit,N=4

Q: Of an initial amount of 8000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

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: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A:

Q: Radium decomposes at a rate proportional to the amount present. If 200 mg. of radium id reduced to…

A: Radium decomposes at a rate proportional to the amount present, so dQ/dt ~ Q so dQ/dt = kQ so from…

Q: Carbon 14 has a half-life of 5,730 years. How fast is a lump of 80 grams decaying after 100 years?…

A:

Q: A species is considered to be endangered if it is expected to be extinct within 20 years. A…

A:

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: Radium decomposes at a rate proportional to the amount present. If half of the original amount…

A:

Q: 2. Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100…

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

Q: a) If an investment grows in value at 2.4% per year, how long will it take for its value to double?…

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: 2. A radioactive material loses 25% of its mass in 10 minutes. What is its half-life?

A: Let No be the initial mass, N be remainingmass.  Then  N= No - 25100 No = No - No4=34NoHence    t…

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: If the half-life of a radioactive substance is 7,300 years, then at what rate is it decaying? (Hint:…

A:

Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: 21. Strontium-87 is used in the study of bones. After one hour, 78.1 mg remains of a 100 What is the…

A: Radioactive decay follows the first-order kinetics. To calculate the half-life of Strontium-87 first…

Q: If a population of is becoming extinct and the population is decaying exponentially. Assume that…

A: From given information

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.