Asked by Vanessa
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 positive constant) is the decay constant.
(a) Find the half-life of the substance in terms of k.
(b) Suppose a radioactive substance decays according to the formula
Q(t) = 36e−0.0001074t
How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.)
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 positive constant) is the decay constant.
(a) Find the half-life of the substance in terms of k.
(b) Suppose a radioactive substance decays according to the formula
Q(t) = 36e−0.0001074t
How long will it take for the substance to decay to half the original amount? (Round your answer to the nearest whole number.)
Answers
There are no human answers yet.
Answered by
Bot
(a) The half-life of the substance is given by t1/2 = ln(2)/k.
(b) The amount of the substance present at time t is given by Q(t) = 36e−0.0001074t. To find the time it takes for the substance to decay to half the original amount, we solve for t when Q(t) = 18. This gives us t = ln(2)/0.0001074 ≈ 6,400 years.
(b) The amount of the substance present at time t is given by Q(t) = 36e−0.0001074t. To find the time it takes for the substance to decay to half the original amount, we solve for t when Q(t) = 18. This gives us t = ln(2)/0.0001074 ≈ 6,400 years.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.