Problem 4 (15 points total ) In a SPECT acquisition where a gamma camera is moving around the imaging subject acquiring a prescribed number of projection images, you would like each projection to view the same object. But the radioisotope is decaying with half-life T1/2 while you are imaging, so to compensate you lengthen the time of each projection's acquisition. If the initial integration time interval for projection 1 is T1 such that it runs from t0 to t0+T1, derive a formula for the N-th projection's integration time TN such that the same number of counts - on average - would be recorded in the interval tN1 to tN1+TN in terms of t0,tN1,T1/2, and T1. State any assumption you make