A piece of charcoal is found to contain 37% of the element B that it originally

Question

A piece of charcoal is found to contain 37% of the element B that it originally had. When did the tree from which the charcoal came die? Use 5600 years as the half-life of the element B. Using a graphing utility, graph the relation between the percentage of the element B remaining and time Using INTERSECT, determine the time that elapses until half of the element B remains Verify the answer found in part (a). The tree died years ago. (Round to the nearest whole number as needed) Choose the correct graph below The graphing window is [0, 40000.5000] by (0, 1, 0 2] The time that elapses until half of the element B remains is years. Round to the neatest whole number as needed.)

Explanation / Answer

a) when did the tree die means we have to find time take to reach 37% of element B.

half life = 5600 yrs ; decay constant , k = 0.693/5600 = 0.00012375 per yr

N(t) = Noe^-0.00012375t

0.375No = Noe^-0.00012375t

t = ln(0.375)/0.00012375 = 7925.89 = 7926 yrs

Half of element remains :

No/2 = Noe^-0.00012375t

ln0.5/0.00012375 = t

t = 5601.189 = 5601 yrs

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