Exponential Growth and Decay

Question

I've been having trouble with a problem. It says:

The radioactive element carbon-14 has a half life of 5750 years. A scientist determined that the bones from a mastodon had lost 51.1% of their carbon-14.

How old were the bones at the time of discovery?

Answer 1

Let A(t) = amount of Carbon-14 remaining after t years = Pe^kt , where P is the original amount

We are given that 0.50P = Pe^5750k

So, 0.50 = e^5750k. Therefore, ln0.50 = 5750k. So, k = -0.00012

A(t) = Pe^-0.00012t (Since 51.1% has disintegrated, 48.9% remains)

0.489P = Pe^-0.00012t

Solve for t.