Can not get part B, followed the solutions manual and get thisanswer. Help Thank

Question

Can not get part B, followed the solutions manual and get thisanswer. Help
Thanks The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by N = N0e-t/tau, where r is the mean lifetime, equal to 2.2 mu s. Suppose the muons move at a speed of 0.87c and there are 5.0 times 104 muons at t = 0. What is the observed lifetime of the muons? mu s How many muons remain after traveling a distance of 3.0 km? Your answer differs from the correct answer by orders of magnitude. muons

Explanation / Answer

The time taken to cover the distance is          t = 3000m /0.87c            =3000m / (0.87 * 3*108 m/s)            =11.49*10-6 s The number of muons           N= No e- ( t / )             = (5*104 ) e -( 11.49 / 2.2) = 269muons

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