The exponential distribution with mean

has cumulative distribution function

Set

the negative of what the book says. Then the probability the atom dies is in one year is

So the book is correct except for the sign.

The book and your teacher are using different interpretations of a decay rate. The mean

of the exponential distribution is interpreted as the expected waiting time to the event, here a decay. So

is the average number of decays per unit of time. Your teacher is says a decay rate of 5.5% means the average number of decays per year is .055. The book says a decay rate of 5.5% means the probability of a decay in one year is .055. These interpretations are different because the average number of decays in one year is not the same the probability of a decay in one year.