# The Journey of X

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• I just stared a new archaeology program at school. I like the program, but I hate the math. ﻿﻿Can you help me?
• I did really well in pre-calc. I can help. ﻿
• What's the Problem?﻿
• What kind of math problems do you need help with? ﻿
• I need help with exponential and logarithmic problems. ﻿
• ﻿Telling the Problem...
• ﻿What's the context of the problem?
• ﻿We found a dinosaur skeleton and we need to see how old it is. We know that it's lost 75% of it's original carbon-14. And we know the half life of carbon is 5730 years.
• We need math in things like archaeology to figure out how long ago animals had died. ﻿
• ﻿The First Equation...
• ﻿Then we need to figure out when the dinosaur died.
• The problems we use to find out the answer to how long ago animals died are logarithmic problems, which use ln. ﻿
• Almost Solved!﻿
• Then we raise P(.5) to x/5730, because that's the half life, right? ﻿
• ﻿In these problems, we need to know how much Carbon-14 it has left, and what the half life of carbon is.
• The Solution...﻿
• We then divide each side by ln(.5), so it's ln(.25)/ln(.5)=﻿x/5730. We mutiply each side by 5730, so that x= (5730*ln(.25))/ln(.5).
• Like she said, the equation to start solving this is f(x)=P(.5)x/h. ﻿
• The equation that we need to use is f(x)=P(.5) x/h. ﻿Then we plug in .25 because 100%-75% is 25% or .25 in decimals. So now we have .25P=P(.5)
• You need to be sure to divide the equation by BOTH SIDES to get x alone. ﻿
• Yes! So now the equation is (.25)P=P(.﻿5)^(x/5730). Then we divide both sides by P to get x alone. Then we take each side and multiply it by ln, so we have ln(.25) =ln(.5^x/5730).
• Teamwork is the best way to solve problems! ﻿
• ﻿So the final answer is x= 11460. That means the dinosaur died 11460 years ago! Thank you so much for your help!
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