example 7
Carbon-14 Dating
During the life of an organism, the ratio of carbon-14 (C-14) to carbon-12 (C-12) atoms
remains about the same. When the organism dies, the ratio of C-14 atoms within its
carcass begins to gradually decrease, but the C-12 does not, so they can be measured to
see how many C-14 atoms were present at death. Comparing the number of C-14 atoms
when it is discovered with the number at death can be used to find how long ago the
organism lived. The ratio of the present amount of C-14 to the original amount t years
ago is given by
y
e
 0.00012097 t
y0
This gives a function
y  f (t )  y 0 e
 0.00012097 t
that gives the amount remaining after t years.
(Source: Thomas Jefferson National Accelerator Facility, http://www.jlab.org/)
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
b. What percent of the original amount of carbon-14 remains after 4500 years?
Chapter 5.1
2009 PBLPathways
During the life of an organism, the ratio of carbon-14 (C-14) to carbon-12 (C-12) atoms
remains about the same. When the organism dies, the ratio of C-14 atoms within its
carcass begins to gradually decrease, but the C-12 does not, so they can be measured to
see how many C-14 atoms were present at death. Comparing the number of C-14 atoms
when it is discovered with the number at death can be used to find how long ago the
organism lived. The ratio of the present amount of C-14 to the original amount t years
ago is given by
y
e
 0.00012097 t
y0
This gives a function
y  f (t )  y 0 e
 0.00012097 t
that gives the amount remaining after t years.
(Source: Thomas Jefferson National Accelerator Facility, http://www.jlab.org/)
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
b. What percent of the original amount of carbon-14 remains after 4500 years?
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways
Amount remaining
Original amount
f (t )  y 0 e
Time in years
 0 .0 0 0 1 2 0 9 7 t
a. If the original amount of carbon-14 present in an artifact is 100 grams, how much
remains after 2000 years?
f (2000)  100 e
 100 e
 0.00012097  2000 
 0.24194
 78.51
b. What percent of the original amount of carbon-14 remains after 4500 years?
f ( 4500 )  y 0 e
 y0e
 0 .0 0 0 1 2 0 9 7  4 5 0 0 
 0 .5 4 4 3 6 5
 y 0  0.58
2009 PBLPathways