Finding half-life from decay rates

[etown]

Measurements of a certain isotope tell you that the decay rate decreases from 8339 decays/minute to 3037 decays/minute over a period of 4.50 days. What is the half-life T_1/2 of this isotope in days?


I know that i have to relate the ratio of decay rates to the ratio of undecayed nuclei present at each time, but i don't know which formula to use to find half life after that.

[Matterwave]

So, the decay rate is simply proportional to the number of undecayed nuclei:

\frac{dN}{dt}=\lambda N

The half life is defined as the time it takes for N to decease to N/2. Can you see where to go from there?