4. phosphorus-32 has a half-life of 14.3days. how long would it take a 50-mg sample to decay to 3 mg

58.0 days

Step-by-step explanation:

The equation for the radioactive decay is

where

m(t) is the mass of the sample left at time t

is the initial mass of the sample

is the half-life

For the phosporus-32 isotope in the problem, we have:

(half-life in days)

is the initial mass

is the mass at time t

Solving for t, we find the time needed for the sample to reduce to 3 mg:

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)