|
|
Exam-Style Questions on Exponential DecayProblems on Exponential Decay adapted from questions set in previous Mathematics exams. |
1. | IB Analysis and Approaches |
In medical imaging, the radioactive isotope Technetium-99m is used due to its short half-life of 6 hours. After being introduced into the body, the isotope decays, and the amount of Technetium-99m present can be tracked over time to study the function of specific organs.
The amount, \( A \), of Technetium-99m present in a patient's body \( t \) hours after injection can be modelled by the equation $$ A = A_0e^{-kt} $$ where \( t \geq 0 \) , \(A_0 \) and \( k \) are positive constants.
At the time of injection, the patient is defined to have 1000 units of Technetium-99m.
(a) Show that \( A_0 = 1000 \).
The time taken for half the original amount of Technetium-99m to decay is known to be 6 hours.
(b) Show that $$ k = \frac{\ln 2}{6} $$.
(c) Medical guidelines suggest that a scan should be performed when the activity of Technetium-99m is between 25% to 50% of the initial dose to obtain a clear image. Calculate the time window after the injection during which the scans should be performed.
If you would like space on the right of the question to write out the solution try this Thinning Feature. It will collapse the text into the left half of your screen but large diagrams will remain unchanged.
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
The solutions to the questions on this website are only available to those who have a Transum Subscription.
Exam-Style Questions Main Page
To search the entire Transum website use the search box in the grey area below.
