Problema Solution
The Mu Alpha Theta members counted 800 of the little creatures at the outset, and after 20 minutes of exponential decay, only 760 remained. What was the half-life of the little creatures to the nearest thousandth of a minute?
Answer provided by our tutors
f(t) = C*e^(kt), where k and C are constants
for t = 0 we have f(0) = 800
C*e^(k*0) = 800
C = 800
after 20 minutes of exponential decay, only 760 remained
for t = 20 min we have f(20) = 760
800*e^(k*20) = 760
e^(k*20) = 760/800
20k = ln(760/800)
k = (1/20) ln(760/800)
k = - 0.0025646645
we need to find the half life that is t such that f(t) = (1/2)f(0)
800*e^(k*t) = (1/2)800
e^(k*t) = 1/2
t = (1/k) ln(1/2)
t = (20/(ln(760/800))*ln(1/2)
t = 270.268 min
the half-life of the little creatures is 270.268 min.