SOLUTION: The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists c

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists c      Log On


   

Question 1157950: The Lualailua Hills Quadrangle of the East Maui (Haleakala) volcano on the island of
Maui in Hawaii is no longer active. To find out the date of the last eruption, scientists
conducted a chemical analysis of samples from the volcano area. The samples
contained approximately 62% of its original carbon-14. How long ago was the last
eruption of the volcano? Use 5730 years for the half-life of carbon-14.
Work must be shown!
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
P=Poe^(-kt)
P/Po=1/2=e^(-kt)
-ln2=-kt
k=ln2/t
=0.693/5730
=0.000121
P/Po=0.62=e^(-0.000121*t)
ln(0.62)=-0.000121*t
t=3950.71 years

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

An equation of the radioactive decay in this case is 


    C%2A%281%2F2%29%5E%28t%2F5730%29 = 0.62%2AC,


where C is the initial mass of carbon-14 in the sample; t is the time in years.


Simplify and solve for "t", which is the major unknown in this case.

Start canceling "C" in both sides.


    %281%2F2%29%5E%28t%2F5730%29 = 0.62


Take logarithm base 2 from both sides


    -t/5730 = log%282%2C%280.62%29%29


    -t/5730 = -0.6897


    t = 5730*0.6897 = 3952 years    (rounded to closest integer value).      ANSWER