HELP Exercise 3 A radioactive substance decays with a halfli

HELP!

Exercise 3. A radioactive substance decays with a half-life of 4 hours. How long will it take until 34mg will have decayed to 10mg?

Solution

half life = 4 hours

so we can write

A /2 = A e^k(4)

1/2 = e^4k

ln 1/2 / 4 = k

k = -0.173286

finding time it takes to decay from 34 mg to 10 mg

10 = 34 e^ (-0.173286 t )

10/34 = e^ (-0.173286 t )

ln ( 10/34 ) = (-0.173286 t )

t = 7.06

so , it takes approximately 7 hours to decay to 10mg