A mixture has two radioisotopes. Nuclide P has half-life $12 min$ and initial activity $2400 dps$ ; nuclide Q has half-life $48 min$ and initial activity $100 dps$ . After how many minutes, to the nearest integer, are the two activities equal?

Numerical answer type, answer in min, tolerance 1.

Answer: 73 min

2400 \times 2^{- t /12} = 100 \times 2^{- t /48}

gives

24 = 2^{t /12 - t /48} = 2^{t /16}

. So

t = 16 lo g_{2} 24 = 16 \times 4.585 = 73

min.