The burial cloth of an Egyptian mummy is estimated to contain 560 g of the radioactive materialcarbon-14, which has a

Lewis Harvey

Lewis Harvey

Answered question

2021-02-12

The burial cloth of an Egyptian mummy is estimated to contain 560 g of the radioactive materialcarbon-14, which has a half life of 5730 years.
a. Complete the table below. Make sure you justify your answer by showing all the steps.
t(in years)m(amoun of radioactive material)057301146017190
b. Find an exponential function that models the amount of carbon-14 in the cloth, y, after t years. Make sure you justify your answer by showing all the steps.
c. If the burial cloth is estimated to contain 49.5% of the original amount of carbon-14, how long ago was the mummy buried. Give exact answer. Make sure you justify your answer by showing all the steps.

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2021-02-13Added 93 answers

Given that
Initially the radioactive carbon-14 present in the burial cloth of the egyptian mummy is 560g.
The half life of carbon-14 is 5730 years.
The total amount of carbon-14 decayed after t years is given by
A=A0(0.5)1h (1)
Where, A0 initial amount of carbon -14
t-time in years,
h-Half life of carbon -14
a) To complete table using the following calculation:
Now,
1) t=0 years, h=5730 years,A0=560g
A=A0(0.5)1h
A=560(0.5)05730
A=560(0.5)0=560(1)
A=560g
2) t=5730 years, h=5730 years,A0=560g
A=560(0.5)57305730
A=560(0.5)1=560(0.5)
A=280g
3) t=11460 years, h=5730 years,A0=560g
A=560(0.5)114605730
560(0.5)2=560(0.25)
A=140g
3) t=17190 years, h=5730 years,A0=560g
A=560(0.5)171905730
A=560(0.5)3=560(0.125)
A=70g
The table becomes
t(in years)m(amoun of radioactive material)05605730280114601401719070
b)To find the exponential function that models the amount of carbon-14 in the cloth, y, after t years:
A=A0ekt
Here, At t=0,y=560 g,
k- rate of decay,
t- time in years.
The exponential function is
y=560ekt
c) To find t, for k=49.5% :
49.5% of original amount of carbon-14 is
49.5%×560=49.5100×560
=49.5×5.6
49.5%×560=277.2g
Now, A0=560, A=277.2 g, h=5730 years, from (1)
A=A0(0.5)th
277.2=560(0.5)t5730

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