Radioactive Decay Model

Question

The half-life of strontium-90 is 28 years. How long will it take a 30-mg sample to decay to a mass of 24 mg? (Round your answer to the nearest whole number.)

Radium-221 has a half-life of 30 sec. How long will it take for 78% of a sample to decay? (Round your answer to the nearest whole number.)

Answer 1

y=ab^x

24=30(1/2)^(t/28)

24/30=(1/2)^(1/28)

0.8=(0.5)^(t/28)

log(0.8)=log((0.5)^(t/28))

log(0.8)=(t/28)log(0.5)

log0.8/log0.5=t/28

-0.969/-0.30103=t/28

0.32189=t/28

t=28(0.32189)

t=9.013 years

100%-78%=22%

22=78(1/2)^t/30

22/78=(1/2)^t/30

0.2820513=(0.5)^(t/30)

log(0.2820513)=log((0.5)^(t/30))

log(0.2830513)=(t/30)log(0.5)

log(0.2830513)/log(0.5)=t/30

-0.54967189/-0.30103=t/30

1.82597=t/30

t=30*1.82597

t=54.779 seconds