calculus

A sample of a radioactive substance decayed to 94.5% of its original amount after a year. (Round your answers to two decimal places.)
(a) What is the half-life of the substance?
(b) How long would it take the sample to decay to 65% of its original amount?

  1. 👍
  2. 👎
  3. 👁
  1. general equation

    amount = starting (1/2)^(t/k) , where t is the time and k is the half-life period

    a)
    .945 = 1(.5)^1/k
    ln .945 = (1/k)ln.5
    1/k = ln.945/ln.5
    k = ln.5/ln.945 = 12.25 years

    b)
    .65 = (.5)^t/12.25
    t/12.25 = ln.65/ln.5 = .621488..
    t = 7.61 years

    1. 👍
    2. 👎
  2. A certain radioactive isotope decays at a rate of 2% per 100 years. If t represents time in years and y
    represents the amount of the isotope left then the equation for the situation is y= y0e-0.0002t. In how many years will there be 93% of the isotope left?

    1. 👍
    2. 👎

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. calculus

    Carbon-14 is a radioactive substance produced in the Earth's atmosphere and then absorbed by plants and animals on the surface of the earth. It has a half-life (the time it takes for half the amount of a sample to decay) of

  3. Physics

    A sample starts with 1000 radioactive atoms. How many half-lives have elapsed when 875 atoms have decayed? I am not sure how to solve this, please help!!

  4. Calc

    A sample of a radioactive substance decayed to 93.5% of its original amount after a year. a) What is the half-life of the substance? ? years (b) How long would it take the sample to decay to 10% of its original amount? ? years

  1. Math

    A radioactive substance decays exponentially. A scientist begins with 130 milligrams of a radioactive substance. After 20 hours, 65 mg of the substance remains. How many milligrams will remain after 24 hours?

  2. MATH Precalculus

    1) A radioactive substance decays exponentially. A scientist begins with 150 milligrams of a radioactive substance. After 26 hours, 75 mg of the substance remains. How many milligrams will remain after 46 hours? 2) A house was

  3. 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

  4. Algebra

    A sample of 600 grams of radioactive substance decays according to the function A(t)=600e^-0.045t where t is the time in years. How much of the substance will be left in the sample after 20 years? Round to the nearest whole gram.

  1. Calculus

    [Exponential growth & decay] The half-life of radioactive strontium-90 is approximately 29 years. In 1965, radioactive strontium-90 was released into the atmosphere during testing of nuclear weapons, and was absorbed into people's

  2. maths

    The half-life of lead is 22 years. How long will it take for a sample of this substance to decay to 80% of its original amount

  3. Math - D.E.Q.

    The half-life of a radioactive isotope is the amount of time it takes for a quantity of radioactive material to decay to one-half of its original amount. i) The half-life of Carbon 14 (C-14) is 5230 years. Determine the decay-rate

  4. Math

    There was a sample of 550 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 5.2% each year. Let t be the number of years since the start of the study. Let y be the mass of the sample in

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