Decay rate,k is 8.1% per year=-0.081. What is the half-life in years???

Question

Can somebody help me with the answer to this question. Thank you and stay safe and blessed to you and your family and friends.

Answer 1

Let A(t) = amount remaining after t years and let P = initial amount.

Then, A(t) = P(1 - 0.081)^t = P(0.919)^t

Find t so that A(t) = 0.5P:

0.5P = P(0.919)^t

0.5 = (0.919)^t

log0.5 = tlog(0.919)

t = 8.2 years