The decay rate of a certain chemical is 9 4 per year What is

The decay rate of a certain chemical is 9 4% per year. What is its half-life? Use the exponential decay model P(t) = P_0e^-kt where kt is the decay rate, and P_o is the original amount of chemical. The half-life of the chemical is years. (Round to the nearest integer)

Solution

k = 9.4% = 0.094

P(t) = Poe^(-kt)

0.5Po = Poe^(-0.094t)

0.5 = e^(-0.094t)

take natural log on both sides:

ln0.5 = -0.094t

t = 7.37 = 7 years is the half life