How long will it take a sample of radioactive substance to d

How long will it take a sample of radioactive substance to decay to half of its original amount, if it decays according to the function A(t) = 450e^-1.057 t, where t is the time in years? Round to the nearest hundredth year. 38.91 yr 70.65 yr 43.33 yr 4.41 yr

Solution

Half of original amt: 450/2 = 225 [A(t)]

450*e^(-0.157t) = 225

divide both sides by 450

e^(-0.157t) = 225/450 = 0.5

then log equiv of exponents
-0.157*t*ln(e) = ln(0.5)
ln of e is one so we have:
-0.157*t = -0.693 =====> t = 0.693/0.157
t = 4.414 yr