The Destruction of Jericho The Bible describes the Exodus as a period of 40 year

Question

The Destruction of Jericho The Bible describes the Exodus as a period of 40 years that began with plagues In Egypt and ended with the destruction of Jericho Archeologists seeking to dates of these events have proposed that the plagues coincided with a huge eruption of the volcano Thera in the Aegean Sea Radiocarbon dating suggests that the eruption occurred around 1360 BC, though other records place the eruption of Thera in the year 1628 BC. What is the percent difference in the^14C (t_vz = 5730 yr) decay rate in biological samples from these two dates? Assuming that the year is 2007, where is the^14C/^12C ratio for the grain harvested in 2007? Radiocarbon dating of blackened grains from the site of ancient Jericho provides a date of 1315 BC plusminus 13 year for the fall of the city. What is the^14 C/^12C ratio in the blackened grains compared with that of the grain harvested in 2007? Calculate the percent decrease in^14C/^12C ratio comparing grain from 1315 BC to 2007 AD. There is additional feedback available!

Explanation / Answer

% decrease = ?

C = A*(e^(-kt))
k = (ln (2))/t1/2

(t1/2 is the half-life)

First we calculate k:

k = (ln (2))/
k = 0.693/5730 = 1.210x10^-4 year^-1

Now we use the first equation to calculate the % :

Here time = 1628-1360= 268
C = A*(e^(-kt))
C/A = e^(-kt)

C/A = e^(-1.210x10^-4 year^-1 *268)
C/A = e^(- 0.032428)

C/A = 0.96809214995 or 96.8 %

% decrease = 100-96.8%

= 3.2%

% decrease = ?

C = A*(e^(-kt))
k = (ln (2))/t1/2

(t1/2 is the half-life)

First we calculate k:

k = (ln (2))/
k = 0.693/5730 = 1.210x10^-4 year^-1

Now we use the first equation to calculate the % :

Here time = 2007-1315=692

C = A*(e^(-kt))
C/A = e^(-kt)

C/A = e^(-1.210x10^-4 year^-1 *692)
C/A = e^(- 0.083732)

C/A =C14/C12= 0.9197 or 91.97 %

% decrease = 100-91.97%

= 8.03%

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