Ask Question
14 January, 14:16

The half-life of a certain substance is 26 years. How long will it take for a sample of this substance to decay to 92 % of its original amount? Use the exponential decay model, A = A_0 e kt, to solve. years (Round to one decimal place as needed.)

+5
Answers (1)
  1. 14 January, 14:26
    0
    t = 3.1 years

    Step-by-step explanation:

    A = A_0 e kt

    Half life (1/2) = 26 yrs

    1/2 = 1_0 e^k. 26

    ln (1/2) = ln (e^26k)

    26k. ln (e) = ln (1/2)

    k = 1/26 * ln (1/2)

    k = - 0.0267

    A = A_0 e^kt

    0.92 = 1. e^ (-0.0267) t

    ln (0.92) = ln (e^ (-0.0267) t

    -0.0267t. ln (e) = ln (0.92)

    t = ln (0.92) / - 0.0267

    t = 3.122

    t = 3.1years (approximate to 1 d. p)
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The half-life of a certain substance is 26 years. How long will it take for a sample of this substance to decay to 92 % of its original ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers