A laboratory is using a radioactive tracer that decays according to the relationship
MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms
Problem
A laboratory is using a radioactive tracer that decays according to the relationship Q(t)=Q0ekt, where Q(t) is the amount of tracer (in microcuries) t days after synthesis.
A chemist measures Q(10)=1.35 microcuries ten days after synthesis. The decay constant k has been independently estimated as k=−0.073±0.002 day−1.
Answer the following in complete sentences, using clear mathematical reasoning rather than numerical calculation.
(a) Explain qualitatively how the calculated value of Q0 changes if the true value of k is at the upper end of its uncertainty interval compared with the lower end.
(b) The chemist claims that the percentage relative error in the computed Q0 is equal in magnitude to the percentage relative error in k. Evaluate this claim and justify your conclusion.