Question #314748

A tumor is injected with 0.9

 grams of Iodine-125, which has a decay rate of 1.15%

 per day. Write an exponential model representing the amount of Iodine-125 remaining in the tumor after t

 days. Then use the formula to find the amount of Iodine-125 that would remain in the tumor after 60

 days.


1
Expert's answer
2022-03-20T06:42:58-0400

Solution: we can use the model for continuous exponential decay

m=m0ektm=m_0e^{kt}

where m0=m_0= 0.9 initial mass

t=t= 60 time in days

k=1.15/100=0.0115k=-1.15/100 = -0.0115 continuous growth rate

e=e= base of natural logarithm

m=m= ending value mass

m=m0ekt=0.9e0.0115(60)=0.9e0.690.4514\therefore m=m_0e^{kt}=0.9 e^{-0.0115(60)}=0.9e^{-0.69} \approx0.4514

Answer :0.4514



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