Calculus

A certain radioactive material decays exponetially. The percent, P, of the material left after t years is given by P(t)= 100(1.2)^-t
a)Determine the half life of the substance

asked by lala
  1. From the equation we can see that the original amount was 100 units
    So we want to know when that amount becomes 50
    50 = 100(1.2)^-t
    .5 = 1.2^-t
    log(.5)= log(1.2^-t)
    log(.5)= -tlog(1.2)
    -t = log(.5)/log(1.2)
    = -3.8

    so t = 3.8 years is the half-life time

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    The rate at which an amount of a radioactive substance decays is modeled by the differential equation dA/dt = kA, where A is the mass in grams, t is the time in years, and k is a constant. Answer the following. a) If a 100-gram
  2. Science

    Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(-t). a) Determine the function A’, which represent the rate of decay of the substance. b)
  3. Physical Science

    A gram of radioactive material has a half-life of one year. After four years how much radioactive material will be left...0g, 1/2g, or 1/4g? None of the above. The answer one-half to the fourth power.
  4. College Algebra

    The half-life of a radioactive material is about 34.6 years. How much of a 1-gram sample of the material is left after 30 years?
  5. algebra

    A radioactive substance decays according to the formula A=A0e^kt where A0 is the initial amount of substance (in grams) A is the amount of substance(in grams) after t years k is a constant The half-life of the substance is 10
  6. Calculus

    The rate of decay is proportional to the mass for radioactive material. For a certain radioactive isotope, this rate of decay is given by the differential equation dm/dt = -.022m, where m is the mass of the isotope in mg and t is
  7. Math

    A radioactive material has a half life of 500 years. A) Given 20 grams of this material, how much will remain after 1,000 years? B) Given 100 grams of this material, how much will remain after 750 years? Thank you to whom ever can
  8. Science

    A material has 32 atoms in all; 24 decayed and the rest undecayed. If the half-life of the radioactive material is 1000 years, what is the age of the material? a. 1000 years b. 2000 years c. 3000 years d. 4000 years
  9. math

    You have just isolated a new radioactive element. If you can determine its half-life, you will win the Nobel Prize in physics. You purify a sample of 2 grams. One of your colleagues steals half of it, and eight days later you find
  10. 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

More Similar Questions