Here is the question give to me by my teacher:

A sample of 137Cs (half-life = 30.1 years) decays at a rate of 10^10 decays per second. How long will it take for the decay rate to decrease to 10^7 decays per second?

The work I have done so far is:

dN(t=0) = -λNo, where dN(t) = Noe^(-λt)

(Although online a website as it as Noe -λt, so not sure if λt should be raised or not)

Because I am trying to find the difference I can make this formula equal to itself:

Noe^(-λt) = Noe^(-λt)

Where:

λ is my decay constant (10^10 and 10^7)

e is e (2.71828)

t is the time (guessing at 0 and x (what the question is asking for))

No is the amount - which I do not know

Overall, the part I am confused with is if this is even correct, and if so how do I find the No of the amounts?