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Bonkmarks People Window Help Do Homework - James Coffee-Tavi https://www.mathxl.com/Student/PlayerHomework.aspx?homeworkld 466665411&questionld-2;&flushed-false;&cld-4860925;¢ James Coffee-Tavi 5/7/18 7:58 ATH 1415 C1601 Winter 2018 omework: 6.8 - Exponential Growth and Decay Models core: 0 of 1 pt 6 of 6 (1 complete) Hw Score: 6.67%, 0.4 of Question Help s only 75% of the carbon-14 expected in living matter, when did th The half-life of carbon 14 is 5600 years. If a piece of charcoal made from the wood of a tree sho tree die? The tree died about years ago. (Do not round until the final answer. Then round to the nearest whole number.)

Explanation / Answer

t(1/2) = 5600 yrs

Right now, it only shows 75% of the C-14

Using formula
A = A0 * e^(-kt), we get

when A = A0/2, t = 5600 yrs,
so plug that in :

1/2 = e^(-k*5600)

ln(1/2) = -5600k

So, k = 0.0001237762822428

So, formula becomes :
A = A0 * e^(-0.0001237762822428t)

Now, at present, it has 75% of the C-14...

So, 75% of A0 = A0 * e^(-0.0001237762822428t)

0.75 = e^(-0.0001237762822428t)

ln(0.75) = -0.0001237762822428t

t = ln(0.75) / -0.0001237762822428

t = 2324.2099959624149998264

So, the tree died about
2324 yrs ago ------> ANS

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