A doctor prescribes 150 milligrams of a therapeutic drug that decays by about 25% each hour. To the nearest hour, what is the half-life of the drug?

Question

help ASAP

Answer 1

general formula is

A=Pe^rt, where r=decay rate. t= hours, P = starting amount

A= ending amount.

for half life use A=150/2 = 75, with P=150

75 = 150e^-.25t decay rate = -25% = -.25

1/2 = e^-.25t

take natural logs of both sides

ln.5 = -.25t

t = ln.5/-.25 = -4ln.5 = about 2.77 hours

half life is about 2.77 hours= about 3 hours rounded to nearest hour

in one hour 150 decays 25% to 75% of 150 = .75(150)=112.5 mg

in 2 hours it decays to .75(112.5) = 84.375 mg

in 3 hours it decays to .75(84.375) = about 63.3 mg

half of 150 = 75 mg

in about 2.77 hours 150 mg decays to about 75 mg