In industrial tracer studies it is often necessary to decide in advance how strong a radioactive sample must be so that its activity reaches a specified value after a fixed time interval.
(a) Starting from the law of radioactive decay, derive an expression for the initial activity A0 required to obtain a desired activity A after a time t.
(b) A petroleum company plans to inject iodine-131 (half-life 8.04d) into a pipeline so that its activity at a detection station 48h downstream is 7.5MBq. Using the result from part (a), calculate the activity that must be injected.
(c) Comment briefly on how uncertainties in the estimated travel time could affect the accuracy of the required initial activity.