A detector is positioned close to a radioactive isotope and registers a count rate of $700\ \text{counts/min}$. The isotope has a half-life of $8\ \text{min}$. The mean background count rate is $60\ \text{counts/min}$. What count rate does the detector record after $16\ \text{min}$?
- A$100\ \text{counts/min}$
- B$160\ \text{counts/min}$
- C$175\ \text{counts/min}$
- D$220\ \text{counts/min}$