Calculus-Modeling Equations

An unknown radioactive element decays into non-radioactive substances. In 420 days the radioactivity of a sample decreases by 39 percent.

1.What is the half-life of the element?

2.How long will it take for a sample of 100 mg to decay to 46 mg?

  1. 👍 0
  2. 👎 0
  3. 👁 2,063
  1. A(t)= Ao* (1/2)^(t/h)
    where h is the half life.
    A/Ao = 1-0.39 = 0.61
    0.61 = (1/2)^(420/h)
    log 0.61 = (420/h) log (1/2)
    420/h = 0.71312
    h = 589 days

    When 100 mg becomes 46 mg of radioactive material, A/Ao = 0.46
    0.46 = (1/2)^(t/589)
    t/589 = log(0.46)/log(0.50)= 1.1203
    t = 660 days

    1. 👍 3
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. Science- Radioactive Dating

    Which of the following statements about radioactive dating is true? a. Radioactive decay is the rate at which new atoms form. b. During radioactive decay, atoms break down, releasing particles or energy. c. The rate of decay of a

  2. Science

    I'm kinda in a rush but take your time!Thx! 1.What was Henri Becquerel studying when he accidentally discovered radioactivity? of black light of X-rays energy 2.When Marie Curie

  3. Science

    When Marie Curie isolated uranium from pitchblende, she realized that the pitchblende was more radioactive than the uranium she had extracted. What did she conclude about her observations? A. Pitchblende itself is a radioactive

  4. Math

    A radioactive substance decays according to the formula Q(t) = Q0e−kt where Q(t) denotes the amount of the substance present at time t (measured in years), Q0 denotes the amount of the substance present initially, and k (a

  1. Science

    How does radioactivity make it possible to understand how Earth can be so old and still have a hot interior? (1 point) A.Radioactive elements trap heat from underground magma chambers. B.Radioactive elements absorb heat from the

  2. chemistry

    The half-life for the radioactive decay of calcium-47 is 4.5 days.If a sample has an activity of 4.00uCi after 13.5 days, what was the initial activity of the sample?

  3. Calculus

    The radioactive element polonium decays according to the law given below where Q0 is the initial amount and the time t is measured in days. Q(t) = Q0 · 2-(t/140) If the amount of polonium left after 700 days is 45 mg, what was

  4. 8th Grade Earth Science Help?

    Which of the following terms refers to the time it takes for one-half of the radioactive atoms in a sample of a radioactive element to decay? - relative age - absolute age - potassium-argon data - half-life** Is my answer correct?

  1. Chemistry

    IF 80mg of a radioactive element decays to 10mg in 30 minutes, the half-life of this element is a.10 min b.20 min c.30 min d.40 min the answer is a.10 min but i would like to know why, please help.

  2. Chemistry

    A 208 g sample of sodium-24 decays to 13.0 g of sodium-24 within 60.0 h. What is the half-life of this radioactive isotope?

  3. Physics

    100g of radioactive element X are placed in a sealed box. The half-life of this isotope of X is 2 days. After 4 days have passed, what is the mass of element X in the box? b) If the box is completely evacuated (perfect vacuum),

  4. Algebra 2 help...

    A half life of a certain radioactive is 36 days. An initial amount of the material has a mass of 487 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 5

You can view more similar questions or ask a new question.