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The trick is that we don't know how much we started with, so we can't plug in a number, so we're still left with N sub 0, we're left with e to the -.00012t, because we don't know how much we started with, we also don't know how much we ended with, but we do know we have 71% of our original amount.So this is our entire amount, if I said we had half of that we would just multiply this by a half.We have 71%, so what I can do is just say .71 times our original amount.If you have and I have 2/3 of the amount of money you have, you take 2/3 times 5.It doesn't really matter that we don't know the exact amount, we're still trying to solve the same exact way.
Archeologists typically use what's called carbon-14 dating to approximate the age of certain things.And how carbon-14 dating works is there is a certain amount of carbon in most elements; in a tree, in a person, whatever it maybe and they know that carbon-14 is a special kind of carbon that decays at a rate that archeologists know.So what they can do is compare the amount that should be in whatever they're looking at into the amount that's left and using a formula which is the exponential decay formula, they can figure out how old something is.So for this example what we're going to be looking at is a stick in King Tuts tomb.They found a stick that had 71% of it's original carbon-14, so they know how much carbons should be in this stick say it's oak or whatever it maybe and there's lots of Math, so they know that some has decayed over time.
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Using carbon-14 dating, so basically exponential decay, and this particular rate, we're supposed to figure out how old the tomb is. So we know our decay formula to be N is equal to N zero, e to the rt and they told us that our rate is a very small negative number and we have 71% of the original amount and we're supposed to find the time, we're supposed to find t.