I'm having an issue because I can't connect my teacher's answer with the textbook's question.
"Tritium is the basic fuel of hydrogen bombs and is used to increase the power for fission bombs. Tritium decays at a rate of 5.5 percent a year. This means that Prob[tritium atom dies <= t] follows an exponential distribution with mean = 1/Log(1-0.055)."
It goes on to explain where it got that answer:
"The formula for the mass at time t is f[t] = e^(r t). Therefore, the average percent growth rate is: [f(t+1)/f(t)] - 1. This simplifies to: e^r - 1. Setting this equation to -5.5, we get r = log (1-0.055)."
I can't see the error in the logic, but the answer doesn't make sense to me. After all, if the rate of decay is -5.5%, why isn't r = -5.5%?
The teacher says a decay of 5.5% means the tritium follows the exponential distribution with mean = 1/0.055.
Can anyone help me make sense of this?