I think the correct form of the equation is given as:
a = a0 * (0.9)^t
where t is an exponent of 0.9 since this is an exponential decay of 1st order reaction
Now to solve for the half life, this is the time t in which the amount left is half of the original amount, therefore that is when:
a = 0.5 a0
Substituting this into the equation:
0.5 a0 = a0 * (0.9)^t
0.5 = (0.9)^t
Taking the log of both sides:
t log 0.9 = log 0.5
t = log 0.5 / log 0.9
t = 6.58 years
Answer:
half life = 6.58 years
