A certain tranquilizer decays exponentially in the bloodstream and has a half-life of 46 hours. How long will it take for the drug go decay to 92% of its original dose?

Question

(A) step one : Find K

K=_________

(B) step two: Use K to determine how long(in hours) how long will it take for the drug to decay to 92% of the original dose

It will take______ hours(round to one decimal place)

Answer 1

1/2 = e^46r

ln(1/2) = 46r

r = ln.5/46 = about -0.0151 = k or r

1 - .92 = e^-0.0151t

.08 = e^-0.015t

ln.08 = -0.0151t

t = ln.08/-0.0151 = -2.526/-0.0151 = 167.27 hours or 167.3 rounded to one decimal

= about 6.97 days

or 6 days, 23 hours and 16 minutes