The general equation for exponential decay is:
Q(t) = Q(0)e^(lambdat)
Where Q(t) is the quantity at a given elapsed time, Q(0) is the initial quantity, and lambda is a decay coefficient
To find lambda given the half-life, you set Q(t) = 1/2Q(0), t = the given time and then solve for lambda
1/2Q(0) = Q(0)e^(lambda(5.27" yrs"))
Divide both sides by Q(0):
1/2 = e^(lambda(5.27" yrs"))
To make the exponential function disappear, we use the natural logarithm:
ln(1/2) = lambda(5.27" yrs")
Replace ln(1/2) with -ln(2)
-ln(2) = lambda(5.27" yrs")
lambda = -ln(2)/(5.27" yrs")
Now we can evaluate at the equation at t= 60.50" yrs" and Q(0) = 1" g"
Q(60.50" yrs") = (1" g")e^(-ln(2)/(5.27" yrs")60.50" yrs")
Q(60.50" yrs") = (1" g")e^(-ln(2)/(5.27" yrs")60.50" yrs")
Q(60.50" yrs") = 3.50xx10^-4" g"
