pre cal question

Question

This exercise uses the radioactive decay model.

Radium-221 has a half-life of 30 sec. How long will it take for 88% of a sample to decay? (Round your answer to the nearest whole number.)

 sec

Answer 1

half life at 30secs. so .5 remains after 30 secs.

88% decayed so 12% remaining. So

.12=.5^t/30

ln(.12)=ln(.5)^t/30

in(.12)=t/30ln(.5)

ln(.12)/ln(.5)=t/30

t=92 secs