Answer to Question #314748 in Calculus for clb

Question

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.

Answer 1

Solution: we can use the model for continuous exponential decay

$m=m_0e^{kt}$

where $m_0=$ 0.9 initial mass

$t=$ 60 time in days

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

$e=$ base of natural logarithm

$m=$ ending value mass

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

Answer :0.4514