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Question

You go to the doctor and he gives you 16 milligrams. radioactive dye. After 20 minutes, 4.75 milligrams of dye remain in your system. To leave the doctor's office, you must pass through a radiation detector without sounding the alarm. If the detector will sound the alarm if more than 2 milligrams of the dye are in your system, how long will your visit to the doctor take, assuming you were given the dye as soon as you arrived? Give your answer to the nearest minute. You will spend minutes at the doctor's office.

Answer 1

Y = Ce^(-kt)

Y = resulting amount

C = initial amount

e = natural log

k = half life constant

4.75 = 16e ^ (-k x 20)

4.75/16 = e ^ -20k

ln (4.75/16) = ln (e ^ (-20k))

-1.214 = -20k

k = - 0.0607

2 > 16e ^ (-0.0607 × t)

2/16 > e ^ (-0.0607t)

ln (2/16) > ln (e ^ -0.0607t)

-2.079 > -0.0607t

34.26 minutes < t

t > 34.26 mins