For this problem. We want to find the age of a piece of bone. And we're told that the, um carbon 14 to carbon 12 ratio, or the percentage of carbon 12 to carbon 14 is 72% of what it was back when the, um organism was alive, um says and were asked to date how old the piece of bone is now. So the first thing that we have to do is figure out the first order rate constant, and we can calculate that by using the half life, which we know to be 5.73 times 10 to the third years. So our equation for figuring out the rate constant K rate constant equals 0.693 divided by the half life. And we were told that the half life is 5.73 times 10 to the fourth years times 10 to the third years. I'm sorry. 10 to the third. There we go. Okay. And based on that, we have ah, the rate constant equals 1.209 times 10 to the minus fourth. And that's in years to the minus one. So that's the first piece of information that we need to know to solve this problem. Okay, then we can use our activity equation. And we know that the log of the activity now divided by the activity at time zero has to equal negative the first order rate, constant times the amount of time that is passed by. So given the problem statement, it looks like we might not have enough information. Do we know what the current activity is? Um and do we know what the initial activity is? Well, we don't specifically know what each of those values are. However, there's a clue up here. That's where this 72% comes in. What the 72% is telling us is that the activity now is 72% of whatever it was initially. So we can convert 72% into a decimal 720.72 and use that in our fraction, replacing hey over a zero. So 0.72 is are a over 80 and that's going to equal negative times. Ah, they're rate constant, which is 1.209 times 10 to the minus fourth years to the minus one, and that times time the time is actually the age of the piece of bone. And when we solve for T. Um, by figuring out the log of 0.72 and then dividing it by 1.209 times 10 to the minus fourth, we find that the time that is past or the age of the bone is roughly 2700 years. So that's how old the piece of bonus.